Let if x < -5 if – 5 3 f(x) and g(x) = / f(t)dt Determine the value of each of the following: (a) g(-7) = (b) g(-4) = (c) g(0) = (d) g(4) = (e) The absolute maximum of g(x) occurs when x = and is the value It may be helpful to make a graph of f(x) when answering these questions.

Q: f(x)=-x^4+20x^3-20x+13 find the intervals where x is f concave up.

A: We find the first and second derivative of f(x).

Q: Find sin2x, cos2x, and tan2x if sinx = 15/17 and x terminates in quadrant I.

A: sinx = 15/17 and x terminates in quadrant I. Now using the identity

Q: Calculate the derivative.

A:

Q: Please show step-by-step solution of the problem.

A: Consider the equation

Q: Find an equation of the tangent line at the given point. (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

A: Consider (x + 2)2 − 6(2y + 3)2 = 3, (1,−1)

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative.

A:

Q: Fill in a table of the following type: f (u) = tan u, g(x) = x4

A:

Q: Calculate y" and y"'.

A: Here the given function as,  

Q: Find the eqation of the line. Line passing through (−1, 4) and (2, 6)

A:

Q: Find the average rate of change of g(x) = −3x^2+2 from x = −5 to x = −1. Simplify your answer as muc...

A:

Q: Find the derivative. dy if y(x) = /x2 +. dx

A: The derivative of the function f(x)=xn is f’(x)=nxn-1.

Q: Calculate without using a calculator. log8 2 + log4 2

A:

Q: An object is thrown straight up with a velocity, in ft/s, given by v(t)=−32t+47v(t)=−32t+47, where t...

A:

Q: Use linear approximation, i.e. the tangent line, to approximate as follows: 0.102 Let f(x) 1 and fin...

A:

Q: Use the Chain Rule to find the derivative. y = (x4 − x3 − 1)2/3

A:

Q: Suppose that the distance an aircraft travels along a runway before takeoff is give by D=(10/3)t^2, ...

A:

Q: Refer to figure 12. Estimate f '(1) and f '(2).

A: At x=1 there is a local minimum. So there f'(x)=0 [there the tangent will be horizontal] Answer: f'(...

Q: Calculate the derivative in two ways. First use the Product or Quotient Rule; then rewrite the funct...

A:

Q: compute the derivative f (x) = 9e−4x

A: Consider the function f (x) = 9e−4x

Q: Find the derivatives of f (g(x)) and g(f (x)). f (u) = cos u, u = g(x) = x2 + 1

A:

Q: A stuntman estimates the time T, in seconds, for him to fall x meters, 15. is T(x) = 0.54Vx. Find th...

A: Instantaneous rate of change – It is the rate of change at each instant in time, not over a long int...

Q: Suppose that the functions q and r are defined as follows.                           q(x) = x^2 + 6 ...

A:

Q: Use the given substitution to express the given radical expression as a trigonometric function witho...

A: Given that, From the figure of the triangle,   Apply Pythagoras theorem  

Q: Refer to Figure 13. Determine f '(a) for a = 1, 2, 4, 7.

A: v

Q: f(x)=Sin(x"+1) f"Cx)= %3D

A: Differentiate both sides by x  

Q: 5. Consider the geometric series (3x )" , determine for what values of x does the series n=0 converg...

A:

Q: Use the Chain Rule to find the derivative. y = tan(θ + cos θ)

A:

Q: Zoom in on a plot of f at the point (a, f (a)) and state whether or not f appears to be differentiab...

A:

Q: Refer to figure 12. Find the slope of the secant line through (2, f (2)) and (2.5, f (2.5)). Is it l...

A:

Q: IATH 1190 SECTION 002-BUSINESS CALCULUS (SPRING 2020 1) 25. Elasticity of Demand Due Friday, Feb 28,...

A: Consider the price - demand equation:    

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on th...

A: We graph the situation using a graphing calculator. The shaded region is rotating about the x axis ...

Q: For y=3x^3+27x^2-9x find the concavity and the x values where the points of inflection occur.

A:

Q: use logarithmic differentiation to find the derivative

A: Consider the given function

Q: work must be completed on a separate sheet of paper. Do NOT write on this ge. Use this page as a cov...

A:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4 ...

A: Using chain rule to compute the derivative for y, consider the solution below.   First of all, consi...

Q: Use the theorems on derivatives to find the derivative of the following function:   f(x) = 52(x(squa...

A:

Q: find an equation of the tangent line at the point indicated. f (x) = 5x2−2x , x = 1

A: At x=1 find f(1)

Q: Use the Chain Rule to find the derivative.

A:

Q: In PreCalculus, how do you use the diamond method, of factoring I mean, when you have ax^2+ bx +c, e...

A:

Q: Compute the limit of the sequence given recursively as follows. If the limit does not exist, enter D...

A:

Q: find the derivative. y = cos−1 t−1 − sec−1 t

A:

Q: Find the derivative. y =(ln(ln x))3

A:

Q: Find an equation of the tangent line at the given point. xy + x2y2 = 6, (2, 1)

A: We first find dy/dx at x=2, y=1

Q: Use the Product Rule to calculate the derivative.

A:

Q: an object moves along the y-axis (marked in feet) so that its position at time t (in seconds) is giv...

A:  Position of the object at time t (in seconds) is given by Now, we know that velocity of object at ...

Q: Use the theorems on derivatives to find the derivative of the following function:   f(x) = 3x2cosx +...

A: Given function is  We know that according to product rule of differentiation, we have (uv)'=uv'+vu'

Q: Find the derivative. y = x ln x

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A:

Q: Sand falls from a conveyor belt into a conical pile (V=1/3πr2h)with a radius that is always one-thir...

A: Let r and h (in feet ) be the radius and height of conical pile respectively at any time t. Then, ac...

Q: Please see attached

A: Marginal profit is the derivative of the profit function.