Use the Mean Value Theorem to prove that f'(x) = 0.01 has a solution in the (-4, -3) interval. Given (picture attached as well): f(x) = (x+3)^3 / (4(x-1)^2 ) = 12 / ((x-1)) + 11/4 + 16 / (x-1)^2 + x/4 f′(x)=((x+3)^2 (x-9)) / (4(x-1)^3) f′′(x)=(24(x+3)) / (x-1)^4

Q: find the function f(x) if f'(x)=(2/1+x2)+(5/7)x5/7 and f(0)=2

A: Given, f'(x)=(2/(1+x2))+(5/7)x5/7

Q: Find the derivative. [5x(x6+1)4]=? Answer is 5(x6+1)3(25x6+1). How did they get this answer?

A: Given

Q: Find f'(x) and simplify. f(x) = 5x4 Inx

A:

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: Find an equation for the line tangent to the graph of 2x f(x) %3D x + 4 at the point (2,…

A: The standard form of the tangent helps to find the required equation. The standard form of the…

Q: Find f'(x) and simplify. X X-19 f(x) = Which of the following shows the correct application of the…

A: Given that       f(x) = x/(x-19)

Q: Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

A: Given function is Differentiating with respect to x , we get

Q: Determine whether the functionf is one-to-one by examining the sign of f' (x). (a)ƒ(x) = x³ + 9x2 –…

A:

Q: Find f'(x) and simplify. f(x) = (0.2x + 2)(0.6x - 9) Which of the following shows the correct…

A: f(x)= (0.2x+2)(0.6x-9)

Q: consider the polynomial f (x) = 7x4- (2 + 2x + 6x2 + 5x3) -8x5. In x = 0.7, use the approximation…

A: Given the polynomial fx=7x4-2+2x+6x2+5x3-8x5 and x=0.7 and ∆x=0.2

Q: Let f(x)=(x-3)/(x2-1).  What can you say about the long-term behavior of f?

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Q: The 7th derivative of f(x) = 3x5 - 12x¹ + 7x³ − 11x² + √5 with respect to a is O 360T O none of the…

A: Topic = Derivative

Q: (B) Use the first derivative test to find the maxima and minima for f(x) = 3. 5z2 + 6x +9. 2.

A: