It is defined as the limit of the ratio of the change in a function to the corresponding change in its independent variable as the latter change approaches zero. A. Constant B. Function C. Derivative D. Domain

Q: use definition to show that the function f(x)= |x|^3 is differentiable at 0, with derivative equal…

A: We have to use definition of differentiable:

Q: Using the definition of derivative that incorporates the idea of limit, prove that if f and g are…

A:

Q: Let f(x) = ? The slope of the tangent line to the graph of f(x) at the point (-2, -) is The equation…

A: Solution:Givenf(x)=9xTo find the slope of the tangent line to the graph of…

Q: Use the limit definition to find the derivative of the function. g(s) =  8 s − 7 g'(s) =  −−8s−72​

A:

Q: Let f(x) =x^3-6x. Calculate the difference quotient f(3+h)-f(3)/h for h=.1 h=.01 h=-.01 h=-.1 #2. If…

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Q: Use the definition of derivative to find f'(x) for f(x) = ax² + 10. f(x+h)– f(x) | f'(x) = lim h0 h

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Q: The following represents the graph of the derivative f'(x) of a continuous function.

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

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Q: Here is the graph of the derivative of a continuous function f: R → R. What would we see on the…

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Q: Use the four-step process to find the slope of the tangent line to the graph of the given function…

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Q: 5. Use the definition of the derivative to find f'(x) if f(x)== x-÷ (i.e. ƒ(x)= . (i.e. f(x +h)-…

A:

Q: Find the derivative by using the definition f(x + h) – f(x) f'(x) = lim where f(x) = v4x +7 h+0

A: given                  f(x)=4x+7

Q: Find, or approximate to two decimal places,the derivative of the function at the given number using…

A: The given function can be differentiated with respect to x. Here the function…

Q: Here is the graph of the derivative of a continuous function f: R R. What would we see on the graph…

A: Given that a graph of the derivative of a continuous function f:R-->R.

Q: Let y=x+∣∣x2−8∣∣. Find the derivative of the function at x=3.

A: Given that y=x+x2-8.

Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: Give two applications of the derivative f(x + h) - f(x) f'(x) = lim h

A: The given function f'x=limh→0f(x+h)-f(x)h is the derivative by first principle.

Q: Let f(x) be a function that is differentiable at x = -2. Given that f'(-2) = 3 and f(-2) = 6, find…

A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

Q: II. Compute the right-hand and the left-hand derivatives as limits to show that the following…

A: Given,

Q: Consider the function f(x) = Va, x > 0. Use the limit definition of the derivative to compute the…

A: Given,           The function is fx=x , x>0We know that,           The derivative of the function…

Q: For f with derivative as in Figure : (a) Is f (c) a local minimum or maximum? (b) Is f a decreasing…

A: The function has local maxima or minima depending upon the first derivative as, If the sign of first…

Q: Construct a first derivative sign chart for f. On which interval(s) is the function f increasing? On…

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Q: Use derivatives to find two positive numbers a and b such that a^2 + b^2 = 1 and such that 2*a+3*b…

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Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: The graph of the derivative of a function is given. y For which x is the (original) function…

A: The graph of the derivative (f') of the graph f is given. Now, the original function f is increasing…

Q: 34. Draw the graph of the derivative. The graph of f (x) is provided.

A: Given

Q: Let y" = e* (g(x)) be the second derivative of y = Determine the value of g(X) if X= -4. (Use three…

A:

Q: Let f(x) = x – 5x. Calculate the difference quotient f(2+h)-f(2) for h = -.1 If someone now told you…

A: Given that

Q: Use the limit formula for the derivative of a function at a point to find f'(-3) for f(r) = 2r2 – r.

A: use limit definition to find the value of derivative.

Q: Suppose that a function f(x) has derivative f' (x) = g(x)+ h(x) for some functions g(x) and h(x).…

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Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: Find the derivative of the function by the limit process. g(t) = t³ + 6t g'(t) =

A: We can find the answer as below.

Q: Give two different interpretations of the derivative of the function y = f(x) at x = a.

A: If f(x) represents a quantity at any x then the derivative f′(a) represents the instantaneous rate…

Q: . Give a function f (x) which tends to 0 as x tends to infinity.

A: We have to find a function which tends to 0 as x tends to infinity.

Q: The graph of a function is shown together with the tangent line at a point P. 10 9. 8. 7 6. 4. 3 2 1…

A: Here from Graph Red line tangent to given function f at point p  so derivative of f is equal to…

Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: Find the derivative of f(x)=axe^(-bx+10) Assume that a and b are constants. f′(x)=

A: If fx and gx are two differentiable function then according to product rule of the differentiation,…

Q: Find the derivative of the function. f(x) : et? + 9

A: This question is about finding derivative of function.

Q: Find the derivative of the function. 4 f(x) x In(x) f'(x) %D

A:

Q: Match the graph of the above function with the graph of its derivative. O O O O O Customize and…

A: Given Graph

Q: Q1) The dervative of the function f(x)= |x+2 using the definition of derivative is

A:

Q: Use the limit definition to calculate the derivative of the linear function. g(t) = 8 − 3t

A: Plug the given function in the limit definition

Q: 6. Use the limit definition of derivative to find f'(x) for the functions below. (a) f(x) = /4r – 1…

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

Q: Use the limit definition to calculate the derivative at x = a of the linear function f(x) = 17.…

A: See the details solution in below

Q: Identify by color which of the graphs on the right is the derivative of the function given on the…

A: The given function was increasing before x= -0.25  So the derivative must be positive for that part…

Q: Use the derivative of a function definition to find f ′(a) at the given number a. f(x) = (5x+6)1/2…

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Q: (a) Find the derivative f'(x) of the function f(x) = (b) Graph f(x) and f'(x) side by side using…

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Q: Find the derivative of the function using the limit definition of derivative.  a. f(x) = 1/(x+3) b.…

A: Consider the given functions

Q: Let y" = e*(g(x)) be the second derivative of y = Determine the value of g(x) if x = -4. (Use three…

A:

Q: Suppose that f(x) = 5x - 2x. Use the limit definition of the derivative to find: (a) The slope of…

A: Given: y=f(x)=5x2-2x To find: the slope of the tangent line, the instantaneous rate of change and…