Tutorial ExerciseFind the derivative by the limit process.f(x) = 15 – x²Step 1Complete the definition of a derivative. f (x) =f(x + Ax) – f(x)limAxAx → 0Step 2Use the definition for the function above to find the derivative.(x + Ax)² – (x2)f '(x) = limAx-0Ax15 - x2 –xAx - (Ax)² –+ x2limAx-0Axf '(x) =xAx - (Ax)?= limAx-0AxlimAx0SubmitSkip (you cannot come back)Viewing Saved Work Revert to Last ResponseSubmit AnswerQuestion 1 of 5View Next Ques

Givenf(x)=15-x2Step -1From the definition of derivativef'(x)=lim∆x→0f(x+∆x)-f(x)∆x

Answered: Find the derivative by the limit…

Math

Calculus

Find the derivative by the limit process. f(x) = 15 – x²

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

See similar textbooks

Related questions

Q: For f (x) = x2 −2x + 5, find its derivative by using the formal (limit) definition of the derivative

A: We have to find derivative using definition

Q: Find the derivative of the function by definition 1 1- f(x) = 2x +3

A: Given f(x) = 12x+3 Consider f'(x) = limh→0f(x+h)-f(x)h= limh→012(x+h)+3-12x+3h=…

Q: Find the derivative of the function by the limit process. f(x)= 2/x2

Q: Use the limit definition of the derivative to find f'(x). f(x) = 3 + 2x – x²

A: Given function isfx=3+2x-x2we have to find the derivative by defination .Formula used :- finding…

Q: 2) Use the limit definition to find the derivative of the given function. y = 3r2 – 2x

A: Limit definition of derivative is f'(x)=limh→0f(x+h)-f(x)h

Q: find the derivative using the appropriate rule or combination of rules. y = e(x2+2x+3)2

Q: Use the limit definition of the derivative to find f'(x) for f(x) = x2 +5 x + 3.

A: the solution is given below

Q: Find the derivative by the limit process. f(x) = 11 – x2

A: We have to find the derivative by the limit process where f(x) = 11 – x2.

Q: Use the limit definition of the derivative to find the derivative of the function 3x – 7 f(x) = %3D…

A: The function f(x)=3x-75x2+1. We have to find the derivative of the given function using the limit…

Q: Use the limit definition of a derivative to find f'(x) f(x)=3x^2+2x-1

A: The formula for the limit definition of derivative is as follows: f'(x)=limh→0f(x+h)-f(x)h

Q: Find the derivative of the function using the limit definition of the derivative. f(t) = 2.5t2 + 6t

Q: Consider the quadratic function y=4-x². Using the limit definition, find the derivative of the…

A: To find the derivative

Q: Given f(x) = 9x2 4x + 11, find f'(x) using the limit definition of the derivative.

Q: y = x*(1 – In x4)

Q: 2. Find y' if y = 5x + 2 using the limit definition derivative.

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the derivative of the following function using the limiting process. f(x) = 1/x2

Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

Q: find the derivative using the definition g(x) = 2x2 + 1

Q: use the Chain Rule to find the derivative. y = e2x2

A: To find the derivative of y=e2x2 using chain rule. Solution: Chain rule of differentiation states…

Q: 3) Find the derivative f(x) = xe-*In(x³) %3D

Q: Find the derivative of the function by the limit process. g(x) = -398 g'(x)=

Q: Find the derivative of the following function using the Limit Definition of the Derivative: f(x) =

A: The given function is:f(x)=3x2To find its derivative using limit

Q: Use the limit definition of derivative to find f (2) if f(x) = V2x + 3.

A: Use the formula for the derivative from limit defination.

Q: Use the limit DEFINITION OF A DERIVATIVE to find the derivative of the function. 16) f(x) = Vx + 5…

A: The derivative of a function y=f(x) is given by f'x=limh→0fx+h-fxh. The given function is fx=x+5.

Q: Find the derivative of the function by the limit process. f(x) = 7x − 3

A: GIven function: f(x) = 7x − 3 Formula used:

Q: Find the derivative using the first principle F(x)= (x-1)(x-2)

A: Given F(x)=(x-1)(x-2) To find the derivative using the first principle From the first principle, we…

Q: Use the f'(x)=limh->0f(x+h)-f(x)/h to find the derivative of f(x)=11x2 AT x=1

Q: For the function given by g (x) = x2 + 2x +1, use the limit definition of the derivative to compute…

A: Please refer the attached image for complete solution.

Q: o f(x) = 4~/x+3

A: by using definition of a derivative.

Q: Find the derivative of the following using the three-step rule 2. y=Va² +x

Q: Find the derivative by the limit process. f(x) = 11-x²

Q: Find the derivative of the function by the limit process. PX) = x - 9x + 1

Q: Find the derivative of the function. G(x) = V1 - 9x² arccos(3x) G'(x) -

Q: use the limit process to find the derivative of f(x) = x^3+4x

A: Given, fx=x3+4x

Q: 2x 3, Use the limit definition of derivative to show that f(x) is differentiable at x2 – 3, r > 2 x…

Q: Find the derivative by the limit process. f(x) = 13 – x2

A: Given that: f(x)=13-x2

Q: Find the derivative of the function by the limit process. f(x) = 31 f'(x) =

A: The given function is fx=31.

Q: Given f(x) = ||+x, at which point does the derivative not exist? Mathematically show that the…

A: According to question given that f(x)=|x|+x"A function f is said to be differentiable at a if f'(a)…

Q: Find the derivative of the following using the limiting process. f(x)= -4x2 + 5x

A: Given: fx=-4x2+5x

Q: the

A: We will find the derivative.

Q: Use the limit definition of the derivative to find the derivative of: f(x) = x^2+5x-2

Q: 2) Find the derivative of g(x) = 4x^2−3x+5 using the limit process.

Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

Q: (2x-6) ¹² 3. h(x)= (3 + نمو)

A: The objective of the question is evaluate the derivative of the given function.

Q: Find the derivative of the function by the limit process. f(x) = x3 - 9x + 1 f'(x)

A: We know,f'(x) = limh→0 f(x+h) - f(x)h by limit processHere,f(x) = x3 - 9x + 1So,f(x+h) = (x+h)3 -…

Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Given fx=x-33x+4

Q: Use the limit definition of the derivative to find f'(x) given f(x) = x² – 3x + 5.

A: Given function :

Q: Find the derivative of the function f(r) = 3x² – 12x by the definition of derivatives | f(x +h) -…

A: here option C is true 6x-12

Question

Tutorial Exercise
Find the derivative by the limit process.
f(x) = 15 – x²
Step 1
Complete the definition of a derivative. f (x) =
f(x + Ax) – f(x)
lim
Ax
Ax → 0
Step 2
Use the definition for the function above to find the derivative.
(x + Ax)² – (
x2)
f '(x) = lim
Ax-0
Ax
15 - x2 –
xAx - (Ax)² –
+ x2
lim
Ax-0
Ax
f '(x) =
xAx - (Ax)?
= lim
Ax-0
Ax
lim
Ax0
Submit
Skip (you cannot come back)
Viewing Saved Work Revert to Last Response
Submit Answer
Question 1 of 5
View Next Ques

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?
FIND THE DERIVATIVE OF THE FUNCTION BY THE LIMIT PROCESS. SHOW YOUR STEP BY STEP SOLUTIONS. 1. f(x) =x²+x-3 2. f(x)= x²-5 3. f(x)= √x+2 4. f(x)= √3x²
Finding the Derivative by the Limit Process In the given question/s, find the derivative of the function by the limit process.:- f (x) =x2 + x - 3
find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the domains of the function and its derivative. must show all steps
Finding the Derivative by the Limit Process In the given question/s, find the derivative of the function by the limit process.:- f (x) = -5x
f(x)=x2+2x-1 g(x)= -500/x, x ≠0 k(x)= |x-2| For each function, do the following: Compute the derivative (that is, the derivative function) by evaluating the limit, for example, lim h →0 f(x+h)− f(x)/h. Show your work. (Notice that for the function k(x), you’ll have to compute the limit differently depending on whether x < 2 or x > 2, and you’ll end up with a piecewise function for the derivative. Since the graph of k(x) is made of straight lines, you can also find its derivative by looking at the actual slopes.)
Use the definition of the derviative to compute the derivative of f(x)= 1-7x2 at the specific point x=2 Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer ). f'(2)=lim→0 (f(2+h)-f(2)) / (h) Part 2: The derivative function Use the definition of the derivative to compute the derivative of the function f(x)1-7x2 at an arbitrary point x=2 Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer). f'(x)= h→0 (f(x+h)-f(x)) / (h) Part 3: The tangent line Now let’s calculate the tangent line to the function f(x)= 1-7x2 at x=5 By using f′(x) from part 2, the slope of the tangent line to f at x=5 is f'(5)= The tangent line to f at x=5 passes through the point (5,f(5)) on the graph of f. (Enter a point in the form (2,3) including the parentheses.) An equation for the tangent line to f…
Use the limit definition of the derivative to find the derivative of the following function. You will not pass this mastery test if you don’t use the limit definition. f(x) = x 2 + 5x − 1
a. Locate the critical points of ƒ.b. Use the First Derivative Test to locate the local maximum and minimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist). ƒ(x) = -x3 + 9x on ⌊-4, 3⌋
lim h--->0 (f(2+h)-f(2)) / h , where f(x)=4x+8
Find the slope of the curve y=x2-5x-4 at the point P(3,-10) by finding the limit of the secant slopes through point P. Can you please show me how to solve?
Discuss the limit of the function as x approaches c and the value of the function as x = c.