The graph of f', the derivative of f, is shown in the graph below. Given that f(-6) = 2, follow the instructions below in order to sketch the graph of f. Plot the initial value on the graph of f. Graph of f *82 6 5 10 Graph of f 12 10 10 8 7 9. 10 10

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A: The given function has four roots. x = -2, 1,5,7. Hence,  f(x) = a(x+2)(x-1)(x-5)(x-7)   At x = 0, y…

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A: Solution:-

Q: Which of the following is the derivative of * f (x) = In(tanhæ)?

A: Given function is : fx=lntanhx To find the derivative of fx tanhx is written astanhx=ex-e-xex+e-x

Q: 6. h(x) = 5cos(a)

A: Given function is hx=5cosx To find: Derivative of given function. Solution: Function is hx=5cosx…

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Q: Consider the graph of y = S(2) shown below in blue. Estimate the value of the derivative at z 1.…

A: The answer is in step 2.

Q: 3. Below is the graph of y = f'(x), which is the derivative for some function f. Using the graph of…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: following

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Q: find the derivative of the following functions

A: The product rule of derivative states that u·v'=u'v+v'u.

Q: Use the Chain Rule to find the derivative of the following functions.

A: To find the derivative of y=1-ex4 using the chain rule. Solution: Chain rule of differentiation…

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A: From the given graph we can see that the slope of tangent to f(x) at x = 1 is close to -1

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A: From the left side of x=1, the derivative is

Q: 1.Find the derivative of the following functions. 2 a) F(x) = ²* 5 √t³ + 8dt et -dt et +3 b) G(x)=…

A: Topic:- application of integration

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A: Given:-               Team A and team B are playing football against each other. x = total  goal…

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists .

A: Given: Use the alternative form of the derivative to find the derivative at x = c, if it exists

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A: The first derivative of ln(x)=1x. The function loga(x) can be written as ln xln a hence its first…

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A: Concept : product rule for derivative is d(f(x).g(x))dx = f'(x) g(x)+g'(x)f(x)  given ddx…

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A: The given function is i) g(x)=1x-1x3 ; -2.5≤x≤-1 and 0.5≤x≤1.5  for g(x)

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A: The function is given by bz = z-52 To evaluate: 1) The second derivative b''z          2) The value…

Q: 1. • Let a be an unknown constant and 1 f(x) = VT + +a. Find the derivative of f(r) with respect to…

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Q: 2. Find the derivative of the following functions: (a). f(x) = x + 4x-2 + 6e" [1 Mark]

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Q: ) For each of the following, use the product rule to find the derivative function. d) f(2) = +1 x2…

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Q: Let f (x) = e10x. %3D Find a formula for the n-th derivative of f, for n 2 1.

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Q: Find the derivative of the following functions.

A: Find the derivative of the following functions.

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A: I have stated the used formulas in the solution

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A: Given problem is :

Q: 6. Use the graph of the function f below to answer the following y = S(x) 2 (a) draw the tangent…

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Q: 2. Use the MVT to show • Prove that the derivative of f(x) = k, on [a, b], where k is constant, is…

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Q: Find the derivative of the following functions at a given point x= a (g) f(x)=- a=4.

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Q: 2Q: For the following data find the first derivative using forward, backward and central difference…

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Q: # 1) Use the given graph to estimate the value of each derivative. Then sketch the graph of f'. www…

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Q: Find the derivative of the function. F(t) = etsin(2t) F'(t) =

A: We can find the derivative as below.

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Q: $) Find the derivative of the function f(z), below. It may be to your advantage to simplify before…

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Q: Find the derivative of the function f(r), below It may be to your advantage to simplify before…

A: The given function is f(x)=ln(e-14x)

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A: We will find out the required critical points.

Q: Find the value of deriVative beloW 3 If x*y5 + x?y³ – xy² + 5y + (x²y+)² = x), then 3y'at(-1,2) = O…

A: derivarive of functions in product and using chain rule of differentition

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: