EXAMPLE 3 If f(2) = 5, (4) = 6, and f(7) = -9, find f -'(6), f ·'(5), and f '(-9). SOLUTION -1 From the definition of f we have f '(6) f '(5) because 6 because f( %3D = 7 because f(7)

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: 12x + 10 Suppose that f(r) = Evaluate each of the following: f'(-2) = 5/2 %3D f' (5) = %3D

A:

Q: f(x) = x2 +9 Find all the values of x for which f' (x) = 0. What is the product of all these values?…

A: To find the values of x such that f'(x)=0 see below the calculation

Q: If f(x) = x² m2. find f'(2).

A: We will use simple differentiation rules to solve these questions.

Q: Can you please answer this question and show all of the steps and say the correct letter

A:

Q: The function f is one-to-one. Find its inverse. 5-4x f(x) = 9x+S -9x + 4 O f'(x) = -8x+5 O f'(x) =…

A:

Q: Find a formula for f-'(x) and (f -1)'(x) if f(x) = V х-2

A:

Q: EXAMPLE 3 If f(1) = 5, f(6) = 7, and f(12) = -10, find f-'(7), f-1(5), and f-1(-10). (Assume f is…

A:

Q: 9. From "First Principles" show that if f(x)= == 2 x²-3' then f'(x) = - 2x (x² - 3)²

A:

Q: 2x? + 5x + 4 (1 point) Find f' (16) if f(x) : f' (16) = -5/2

A: here is quation of derivative we have to derivate function F(x)= 2x3/2 + 5x1/2 + 4x-1/2 f'(x)=…

Q: 7x² + 3x + 3 If f(x) = then: f'(x) =| f'(3) =

A: Given function fx=7x2+3x+3x To find the derivative of given function Quotient rule is used For any…

Q: r 4-5x 3. f(x)=- ; f'(-1)

A:

Q: f(x) then: f'(x) = f'(1) -

A: We are asked to find the derivatives of the function.

Q: Find f'(x) for f(x) = - 3x + 4) Do not simplify. x3 - x2 + 3x Select one: O A. 6(x3 - x2 + 3x)(3x +…

A:

Q: 49 For f(x) = x − ², x < 0, find (ƒ−¹)'( ), find (ƒ-¹)' ( -5 ) 49 (F-¹) (-42) - (ƒ−¹) 5 help…

A: Topic:- application of derivatives

Q: 4+ (-1.9, 2.8) f(x) = x - 3x - x 5 -4 -3-2 -1 1 2 3 4 -3- -4 (a) (b) gure 3.21 (a) One section of…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: The graph of a continuous function f : [0,9] → R is given below. The function

A: given F(x)=∫0xf(x)dx

Q: If F'(x) = f(x) and F(0) = 0, find F(b) for b = 3, 5, 7, and 9.

A: Given graph of f(x)

Q: Suppose f(x), f'(x), g(x), and g'(x) have the values shown: -6 I -7 f(x) -9 f'(x) -1 g(x) 10 g'(x)…

A:

Q: The graphs of f(x) and g(x) are shown. For what values of x does f(x) = g(x)? x = -2, x = 0, x = 3…

A: We have to choose correct option

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

A:

Q: 7x-2 , find f (x). Answer: (Correct to 3 decimal places) f'(x) = (-5 x + Let f(x) = %3D -4x-5 1)/(_…

A: fx=7x-2-4x-5 Now let y=7x-2-4x-5

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.