8. Given that |f'(x)| < 1/3 for all x, and f(4) = 0, what can you say about the value of f(10), and why?

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

Q: 2. find the high er order derivative of the given funcion witch whi ch Equal to 2ero f (x) = = x°-…

A: If we have a function f(ax) then the derivative of the function will be,     Here it is given that,

Q: What is the first derivative of the following function: f(x) = (x³ + 2)4 O f'(x) = 12x²(x³ + 2)³ O…

A:

Q: Next, we solve for values of x that make f'(x) = 0. These are called critical values. (Note: There…

A: Given               f'(x) = x2-4x+4  we know that,                              f(x) has critical…

Q: 1) Find the derivative of the given function with respects to e 3 tan 6 In 3 y

A:

Q: 8. the second derivative of f(x) =3e^5x , is а. 15е^5х b. 125e^5x с. Зе^5x d. none of the other…

A:

Q: 18 The derivative of the function f(x) = x² + is 18 4x3 + (æ³) 18 O 4x³ - (æ²) 18 4x° + (x) 4x + 18…

A: d/dx(xn)=nxn-1 Given f(x)=x4+18/x  To find the derivative of f(x) differentiate once

Q: 4) Calculate the first derivative of the following functions: 1. f(x) = In 2x2+1° 2. f(x) =…

A:

Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: In the given equation/s as follows (a) find the critical numbers of f, if any, (b) find the open…

A: Given, f(x)=x23-4

Q: Find the critical points of the following function. f(x) = 5x? - 3x – 1 What is the derivative of…

A:

Q: The actual error when the first derivative of f(x) = x - 3ln x at x = 3 is approximated by the…

A: Solution:-

Q: What is the first derivative of f (x) = ln n A)? 3x²+7x 5х Select the correct answer below: бх-7 O…

A: Given query is to find the derivative of the expression.

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

A: Answer

Q: 2 3 Use the first derivative test to determine the local extrema, if any, for the function f(x) =…

A: Take the derivative of f (x)  and equate to zero for finding point of extrema.

Q: (a) Suppose that the first derivative of the function y = f (x) is given by f'(x) = 6(x +1)(x – 2)²…

A:

Q: 12. Consider the function f (x) = sin (nx). On the interval [0,3]. At what value of x would the…

A: Topic = Derivative

Q: 4. Find the equation of the tangent line and the normal line to the graph of the given function at…

A:

Q: Find the critical points of the following function.   f(x) = 1/x - ln(x)

A:

Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

A:

Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

A:

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

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: In the given equation/s as follows (a) find the critical numbers of f, if any, (b) find the open…

A: The given function is;  f(x)=x2-8x differentiate with respect to x f'(x)=ddxx2-8x

Q: 1) The derivative of f (x) = e2x² cos x is: 2) Simplifying the expression e n(4x-3) + eln 2x In(e3x)…

A:

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

A:

Q: Suppose that the first derivative of f(x) = x² In x is approximated by the following formula f'(x) ≈…

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = In x²;…

A:

Q: Find the actual error when the first derivative of f (x) = In x at x = 2 is approximated by the…

A: given  fx=lnx f'x≈fx+h+2fx-3fx-h4h to find the actual error

Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

A:

Q: 2.) f(x) = (x5 – 2x³ + 1) 3

A:

Q: 4)Find the inflection points of the function . f(x)=ln(x^(2)+1)

A: In this question we will find the point of inflection   we have given function   f(x)=ln(x2+1)…

Q: In(4x Given f(x) = the derivative f'(x) is 4 1 4x 1 4x O 4 O z4z

A:

Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

A:

Q: What is the critical point of the function g (x) = (x ^ 2/2) + x (ln (x) −1), using Newton-Raphson,…

A:

Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: What is the first derivative with respect to x of the function g(x) = 3/9x O 1/2 9.

A:

Q: What is the first derivative with respect to x of the function g(x) = 3/9 9. O 1/2

A:

Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

Q: 6. Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x)

A: Slope of tangent is obtained by derivative of the function f(x).

Q: 2. Find the first derivative of the following expression: f(x) = (x2 + 1)sin a

A: take derivative  use the exponent rule

Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: Derive the following formula for approximating the derivative f": 1 f"(x) ≈ (-f(x+2h) + 16f (x + h)…

A: Given: The formula is f'(x)≈112h -f(x+2h)+8f(x+h)-8f(x-h)+f(x-2h). To prove: The given formula. To…

Q: 10 The derivative of the function f(x) = x7 + - 10 726 + (r³) 10 71° + (2) 1 10 7x + 10 10 726 (z²)…

A:

Q: Monday, 1) Find the derivative of the given function with respects to e y = 3lan® In 3

A:

Q: x² +2x+1 6.) f(x) = 3

A: The given function is f(x)=x2+2x+13. Find the first derivative or f'x of the functions by using the…

Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…

Q: 1.) f(x) = (2x + 1)(3x – 2)

A:

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

A: The given functions are: fx=2x2-1x2+3x2+1 and gx=x2+872-3x25 The person's brother believes that,…