Problem 7. Let f(x) be a differentiable function and suppose that 3 < f'(x) < 5 for all values of x. Show that 18 < f(8) – f(2) < 30.

Q: Problem 1. Find the critical numbers, intervals of increasing and/or decreasing of the following…

A: y=f(x) We will get first derivative test which is equal to zero f(x)=x23-4f(x)=-x6+6x10

Q: 3. Given f(x) = x + 2 and ƒ '(x) = give the equation of the tangent line to %3| 2Vx(x+2)² f(x) when…

A:

Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: Problem 4 Let f(x) = 1 Use the limit definition the derivative to find f'(x). Then state the domain…

A:

Q: Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of…

A: As per the instruction, we will be answering only question 2. Given: For (a), From the given…

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: 1) Let f be a differentiable function that passes through the point (2, 3). Suppose g(x) = f(Vx) and…

A: First note that slope of tangent is given by the derivative of that function at that point.…

Q: QUESTION 2 Let f(x) be a function with second derivative of f"(x) =(x+8)(7x –11)(x – 13). Determine…

A:

Q: For what value of the constant cis the function f continuous on(-0,0) x2+ 2x +6 if xsZ cosin (x-2)…

A:

Q: In problems 16-19, each limit represents the derivative of some function f at some number a. State f…

A: This question can be solved using the concept of derivative of a function y=f(x) at a given point…

Q: Suppose that the differentiable function y = ƒ(x) has an inverse and that the graph of ƒ passes…

A: Given,

Q: Please use Limits this is under calculus section

A: When x = 2, y = g(x) = 4 / (x - 1) = 4 / (2 - 1) = 4Hence, the point of tangency is (2, 4)

Q: 1.2. Find the x-values for any points on the curve y =f(x) with horizontal tangents. 1. Let f(x) =…

A:

Q: Problem 3. a) Find the critical numbers of f(x); b) find the open intervals on which the function is…

A: fx=4x2-8x a). Critical numbers are the numbers at which first derivative is zero. So differentiating…

Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: Problem 4: Perform a first derivative test on the function f(x) = 2x + 6x a) Locate the critical…

A:

Q: 5. Suppose f(3) = -2, g(3) = 5, h(3) = –1, f'(3) = -4, g'(3) = 3, and h'(3) 2. Find the value of the…

A:

Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.

A:

Q: Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of…

A: This question is based on application of Derivative.

Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Problem 5  Find the derivative of the following function using the Fundamental Theorem of Calculus.…

A:

Q: Suppose that f is a differentiable function with f(2)=5. If the tangent line to the graph of y= f(x)…

A:

Q: Problem 4  Find the derivative of the following function  F(x)=∫ (t^2)/(1+(7t^4))dt Upper limit of…

A:

Q: 1. Below is the graph of f(x) = |x]. Using the left side of the function with the equation y = – x,…

A: The graph of fx=x is given. The equation for the left side of the graph is y=-x and the equation…

Q: 3) State the critical points of the function g(x) = (x – 9) 23

A: A critical point occurs when the derivative is 0 or undefined.

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

A:

Q: Problem 3 Let f(r) = x² + r. Use the limit definition of the derivative to compute f'(2). Find an…

A:

Q: Problem #4 Perform a first derivative test on the function f(x) = x V25- x2 from[-5, 5] by doing the…

A:

Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

A:

Q: True or false: The maximum value of the function y = -2 cos x + 5 is 7.______

A:

Q: 4) Find the values of x where the tangent lines to the graph of the function is horizontal. f(x) =…

A: a) Consider the function fx=xx2+16. To identify the x values where the tangent lines to the graph of…

Q: Optimization Problems 1) Let f(x) = 12+2x² – x*. Use the second derivative test to classify the…

A:

Q: 3. If f(-1) = 3, f'(-1) = 5, g(-1) = -1, gʻ(-1) = 2, let h(x) = f(x) g(x). Find an equation for the…

A: given: f(-1)=3, f'(-1)=5, g(-1)=-1 and g'(-1)=2 h(x)=f(x)g(x). we have to find the equation of the…

Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1.…

A:

Q: Question 1 Find a classify the critical points of f(x)=-, using the two methods we learned in class:…

A: The given function is :f(x)=x55-x33 To find: Critical points of f, and  we need to classify them…

Q: Suppose we know that f(x) is continuous and differentiable on the interval [1, 9], that f(9) = 0 and…

A: Given, f(x) is continuous and Diferentiable on interval [1,9] f(9)=0 and f'(x)≥8 We have to find :-…

Q: In Problems 35-40, find f' (x) and the equation of the line tangent to the graph of f at the…

A: Given query is to find the equation of tangent line.

Q: Let f(x), g(x) and h(x) be the functions from Problem A.1. Find the derivative of the following…

A: Recall:  Product Rule:   d dxf(x).g(x)=f(x).g'(x)+g(x).f'(x)   Given, derivative(x) = f(x) . g(x) +…

Q: Question 3 Consider a differentiable function g with domain [0, 0). Given that g'(x) = a e" and…

A: If g'' is negative then x is point of maxima if g'' is positive then x is point of minima

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: 11. Suppose that f(x) is differentiable everywhere and we know that f(-4) f'(x) > 6 for all x. = -2…

A: Given, fx is differentiable everywhere. f-4=-2 f'x≥6, for all x dydx≥6, for all x  dy≥6dx…

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: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: Problem 1: Consider some arbitrary function f(x), whose value and whose derivative values of every…

A: Notice that g(x) is 0 at x=1.

Q: 2, Problem 6. Below is the graph of the derivative of a function f(x). 1.2 0.8 y 0.4 -2.4 -1.6 -1.2…

A:

Q: 3) Suppose g(x) is a differentiable function such that gl-4) = 0 and g'(-4) = 3. Find an equation to…

A:

Q: Problem 1: Consider some arbitrary function f(x), whose value and whose derivative values of every…

A: The following concepts are used to analyse the linear approximation of the function. The graph of a…