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: Given the equation x' = -4yf (x) + sin(y) + 1. Take the derivative for both sides of the equation…

A: Given equation is x3=-4yfx+siny+1 Product rule of differentiation states that: ddxuv=vddxu+uddxv…

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

Q: For each of the above functions, prove that f(f-1(x)) = f-1(f(x)) = f(x) = +6 f(x) = x3 + 2 f(x)…

A:

Q: 9. f(x)=T √√5x²

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 the derivative of f (x) = V3x² In(3x²). 2/3x2 A 3x In(3x²) + V3x2 2 + 3x In(3x²) В

A: Given thatfx=3x2ln3x2To find : derivative of…

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: a) y = −8x² + 4x¯¹ − 2 b) f(x)=√√x - √x 5 c) g(x) = x³

A:

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: 2. a) Find and fully factorise the derivative of f(x) = (2x + 1)2 using expansion and the power…

A:

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: Use the Chain Rule & Power Rule to complete the first line ONLY of the derivative for g(x) = (5x³ —…

A: The function is given by gx = 5x3-x44 To determine: The expression of the first derivative.

Q: 1. Find the derivative of the following: a) 3x²+6x f(x)= 5x-1

A: according to bartleby guide line we do only first part of multiple questions…

Q: 11. f(x) = 4x³ In(5x² +1)

A: Topic-Derivative of a function We are given,f(x)=4x3ln(5x2+1)we know…

Q: Find f'(x). 4 f(x) = 3x5 (x² - 4) X

A:

Q: Find f'(x) of f(x) = 3π√123

A: given: fx=3π123 we have to find f'(x)

Q: If point P (4,-3) is on f(x) and if g(x-2) = -3f(1-x) -5 , then determine the point P' on g(x).

A:

Q: Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two…

A: Given function, f(x)=x2-3x-18

Q: Find an anti-derivative F(x) of f(x) = 7x³ – 6x² –- 1 satisfying that 7 F(1) = 4

A: