Let xo = 0.5. Given 1 f(x) = -2ex + 4x² ELL f'(x) = 2e-x + x³ 1 1 1 120 x -x5 + 2x 24 1 ƒ"(x) = −2e¯* + 3x²-x f(4)(x) = -2e-* +6-x f(5)(x) = 2e-x-1 f(6)(x) = -2e-* 6 + 2 1 2 f''(x) = 2e-x + 6x - x² 2 x3 a. Find the Taylor Polynomial, T3 (x), of degree at most 3 for f(x) expanded about xo. b. Give the general error formula for f(x) - T3(x) for any x. c. Find the absolute error in using T3 (0.65) to approximate f(0.65). d. Use the error formula to find a bound for the absolute error in approximating f (0.65) with T3 (0.65).

Q: 4 X- - 5x +4. %3D Find f'(x), f"(x), and f (x) for f(x) = f'(x) = f"(x) =

A:

Q: Suppose that 2 < f '(x) < 4 for all values of x. What are the minimum and maximum possible values of…

A: (a) Given that 2≤f'(x)≤4 for all values of x. By mean value theorem, if f(x) is continues in a,b and…

Q: Differentiate. x2 -9 f(x) = In f'(x) = O

A: Explanation: Given that,  f(x)=lnx2-9x

Q: If f(x) = 7+ Find f'(x). Find f'(x). 10/8 + 4 x²

A: Given that a function f (x) = 7+ 5/x + 4/x2.  And we find f'(x) and f"(x).

Q: x-²²-3 ²-3, determine the x-value(s) where f(x) changes from concave up to concave down. f(x)= Ox=…

A:

Q: 3x + 6 If f(x) find: 2x +2 f'(x) = f'(3) =

A:

Q: Find invers of function f(x)=1/2x+1

A:

Q: if f(x)={ -3x       for x -1  find f(-2)  a. -6 b.9 c.6  d.-1 e.0

A:

Q: Identify x-values where f"(x) > 0. (Enter your answer using interval notation.) Identify x-values…

A:

Q: If 11 +3f(x) + 8x²(f(x))' = 0 and f(1) = -1, find f' (1). f'(1) =

A:

Q: 4x + 2x - If f(x) = | find f'(x) x4

A: Given that, f(x) = (- 4x5 - 4x4 + 2x3) / x4 And we have to calculative the first derivative of the…

Q: a. f(x) = 5x +9x³ +12x² - 7x f'(x) = b. f(x)= 0.03x² -0.4x+10 f'(x) = b. f(x) = 10x³ +5x*-8x f'(x) =

A:

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: Find f. f(x): = f"(x) = -2 + 30x - 12x², f(0) = 5, f'(0) = 12

A:

Q: If 87 + 2 f(x) + 3x² (ƒ(x))³ = 0 and ƒ(1) = −3, find ƒ'(1).

A: 87+2f(x)+3x2(f(x))3=0,f(1)=−3

Q: If f(x) = 6 + 5x > Next Question 5x², find f'(-1).

A: We have to find the value of f'(-1).

Q: Given f (x) find f^−1 (x) for each of the following:  f (x) = 2x−3/7+x

A: Given function is:

Q: Given h(r) = 1/r+8, find the following.  h(x^2)+1

A: We have to solve the given questions

Q: Suppose f'(x) = 8x³ + 12x + 2 and ƒ(1) = −4. Then f(−1) equals . (Enter a number for your answer.)

A:

Q: If f'(x) = 2x³ + 3x² − 4x + 5 and f(0) = 1 and f'(0) = 2 find f.

A:

Q: Consider the following. f(x)=x²-6x² + 7

A: