Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.                         Function f(x) = −1/2 + 7/5x3              Point (0, −1/2)

Q: Find the slope and the equation of the tangent line to the graph of the function at the given point.…

A: Given,f(x)= -2x +5 and the point (1-,7)

Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: Given that, f(x) = 3x - 7 Then we get, f'x=limh→0fx+h-fxh

Q: Find the derivative of the given function. 3-2х y = 3+2x

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the derivative of h(x)=(−2x−5)6 /(2x−3)3   You should leave your answer in factored form. Do…

A: Calculation:The given function is h(x) = (-2x-5)6 / (2x-3)3.Obtain the derivative of the function…

Q: 1. f(x) = x² at x = 3

A: Given: f(x)=x2 at x=3

Q: Find derivative of the function f(x)=x power3 -1/x-1

A: By applying the chain rule and quotient rule we find the derivative of a function.

Q: (1) Using the definition of derivative, find the derivative of the following functions: (a) y = xVx2…

A:

Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: fx=32x Now,…

Q: Find the derivative of the function.. 8 7 h(x) 218 4 х - h'(x)=

A: To find the drivative of the given function y=h(x)

Q: Use the definition of the derivative to find the derivative of the function h(x) = x+3 then find the…

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Q: Use the General Power Rule to find the derivative of the function. g(x) = v6- 7x

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Q: Find q' (x) from q(x) = -5x³ + x2 – 3x – 3 using the definition of a derivative. (Do not include "q'…

A: Given, q(x) = -5x3 + x2 -3x -3  Differentiating q(x) with respect to x  d[q(x)]/dx = q'(x) q'(x) =…

Q: Find the derivative of the function. g(x) = 2(3 - 8x) g'(x)=

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Q: Q2/ Find the derivative of the function (x) =v3x-x by definition

A: Solve the limit for very small change in x .

Q: y = x³ – 3x2 + 3

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Find the derivative of h(x)=(-2x-5)3 (2x-4)5you should leave your answer in factored form. Do not…

A: Compute the derivative of h ( x ) as follows.

Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3) when the…

A: Given function: fx=-x2+2x-3 Find the derivative of f(x) The formula for f'(x) is given as…

Q: Find the derivative of the function. 2 + g(x)

A: We know that  ddxxn = n·xn-1

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A:

Q: Use the rules for derivatives to find the derivative of function defined as follows. y = -4x-3

A: Given: y=-4x-3

Q: a) Find the derivative of g(x) = 3tanx - 4cotx. b) What is the value of g'() ?

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Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

Q: In the given equation/s , find the slope of the graph of the function at the given point. Use the…

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Q: Find the derivative of the function. g(x) = 3(4 – 7x)* g'(x)=

A: We have to find g'(x).

Q: Using the definition of the derivative, find ƒ′(x) . Then find ƒ′(−2) , ƒ′(0) , and ƒ′(3)  when the…

A: Given: fx=2x3+5 To Find: To find f'x and then to find f'-2, f'0 and f'3.

Q: Consider the function: y = -3x3ex Find the first derivative of the above function.

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Q: Given f(x)=√x + 3, find f'(-2) using the definition of a derivative. Provide your answer below: ƒ'(…

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Q: Find the derivative of the function. t(x) = x2 − 8x3  / x

A:

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: It is given that,f'x=-2x8-x2     and point 2,9 We have to find the function.

Q: Use the Quotient Rule to find the derivative of the function. 2х — 3 g(x) x - 1 g'(x) = %3D

A: Given that gx=2x-3x2-1

Q: Q3: Using the definition of the derivative to find the derivative of the function y =

A:

Q: Find the derivative of y=x2(x3-1)5

A: The given function is: y=x2x3-15

Q: Find the derivative of the function. g(x) = 2(3 – 7x) g'(x)=

A:

Q: Use the Chain Rule to find the derivative of the function. Use positive exponents in your final…

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Q: Find the derivative of the function g(x) = .5 3x + gʻ(x) =|

A: To find the derivative of the given function

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A:

Q: Find the derivative of the irrational function y=2√x−33√x.

A: Given: y=2x-33x

Q: a. Use the definition of the derivative to show that the derivative of f(x) = 4x² - 2x+1 is 8x-2. b.…

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Q: Find the derivative of g(x) = 3x2-1/(2x+5) using the Quotient Rule. Simplify your answer, if…

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Q: The graph of function f(x) is shown below. At which value of a is the derivative of the function…

A: The graph of the function

Q: Find the derivative of the following function by applying the definition of the derivative. State…

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Q: Use the definition of the derivative to find the derivative of the function g(x) = 4 –x², then find…

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Q: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

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Q: '(a): Using the definition of derivative, find the derivative of f(x) = x² + 1.

A: The given equation is: fx = x2 + 1 The derivative of this equation is found as follows:

Q: х3 — f(x) = 2x2 + 2 x²

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Q: Find the derivative of the following functions. Show your solution.

A: As per our guidelines we are supposed to answer only one question. kindly repost others question as…

Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: f'x=-2x8-x2    passes through the point2,2x,y=2,2Indefinite integral:∫f'x dx=Fx+C

Q: Find the derivative of the function. g(x) = 4eVx g'(x) =

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: