5. Since /1+ f'(x)² > 1 for any function f, we have length of graph of y = f (x) over [1,4] = 1+ f'(x)² dx 1dx = 3

Q: Let f(x)=4x^(3)- 8 Find f '(4)

A:

Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: Ex+ 8x3-72x?+4 三X'

A:

Q: 3. Find f'(x) for f(x) = 3x-4 2x+3

A:

Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: Consider the following function: Step 1 of 4: Determine ƒ'(x) and ƒ"(x). f(x) = (x − 1)(x+8)² Answer…

A: Step 1:To determine f′(x) and f′′(x) for the given function f(x)=(x−1)(x+8)2, we can use the product…

Q: (8 points) Find the slope of the line tangent to the graph of 1 f (x) = 2x* – 32x + 17x2 – 9x + 4 at…

A:

Q: 3 =-=—= x³. - 4x² + 16x + 14 with tangent lines parallel to the line 20x - 5y = 2. Find all points…

A:

Q: Find f. f"(x) = -2 + 36x - 12x2, f(0) = 2, f'(0) = 18

A: Given, .Given,  f(0)=2, f'(0)=18.We know,

Q: determine the f(0) if f'(x) = 2cosx + 8x^3 + e^x

A:

Q: If f(x) = 7+ f'(x) = Find f'(3). ƒ'(3) = 5 X + 2 x2 I find f'(x).

A:

Q: Find f. f"(x)  =8  x3 + 5   , f(1)   =  0 , f'(1)  =8

A: It is given that, f''x=8x3+5,  f1=0, f'1=8.   Integrate the function f''x=8x3+5 as follows".…

Q: Find f '(x). f0) = (+4)5 f(x) f '(x)=|

A:

Q: F(x)=-4cosx-9tanx , f’(4pi/3)= ___

A:

Q: f'(x) 6 48 3 8 Write down the value(s) of x for which the original function y = f(x) is a.…

A:

Q: y' = 8|x| = - 8x, x≤0 8x, x>0

A: To find y'' and graph the general shape of f(x), we first need to integrate the given expression for…

Q: Let f'(x) = x³ - 9x² +24x +3.

A:

Q: Use the graph of y = f' (x) to fill in the missing information.

A:

Q: y" – 12y" + 32y = 42e",

A:

Q: Find f. f'(x) %3D 6х — 3/x*, х> 0, f(1) %3D 6

A:

Q: f(x,y)= 3xy / (x^2+ 2y^2) find the range and graph

A: It is given that fx,y=3xyx2+2y2. The objective is to find the range of fx and to graph it. The…

Q: Find f. f(x) = f'(x) = 24x² + 2x +4, f(1) =1, f(1) = −4

A:

Q: Given f''(x) = 3x – 6 and f'(– 3) = – 2 and f( – 3) = - 1. Find f'(x) = and find f(4) =

A:

Q: Q12. If fla)= tann- 3 secu find f'(a) = find f'E) =

A: first derivative of f(x) is f'(x)= cos x+3sinx

Q: What is the f'(1) of the function f(x)%3D foralla #-1 x+1

A: We have to find