For the function y = 4x- 16x2 %3D a. Use the first derivative test and sign diagram OR first and second derivative test to determine the maximum and minimum turning point coordinates b. Determine the coordinates of point of inflections C. Determine the coordinates of global maximum and minimum points when the domain is [-1,1.5]

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: In the feasibility test, the flight movement of a drone is known to have a position function height…

A:

Q: Given the derivative f′(x), find the x-value for all relative extrema for the graph of the original…

A: Answer

Q: The temperature in degrees Celsius (C) in Toronto starting on March 1** can be represented by the…

A:

Q: Graph the function f(x) = coordinates are -2,0, and 1. 2a? and draw the tangent lines to the graph…

A: Sketch the function.

Q: Examine the following functions for maxima-minima and trace the curve a. Y=x* + 1 a?x b. Y= a² –x²

A:

Q: Given the function f(x)=x^3+9x^2+19x+4, determine all coordinate points (x,y) on the graph of f such…

A: Differentiate the given function and equate to -5 and find coordinate points.

Q: Consider the following function h(x) = -3r – 5x* + 20z³ + 60x. Find the point on the graph of h(x)…

A:

Q: Q4) Determine slope of a curve y = x* +1 at x = 1

A:

Q: The average price paid by the synfuel industry for a short ton of coal between 2002 and 2005 can be…

A: The price of coal p(t) (in dollars) paid by the synfuel industry as a function of time t (in years)…

Q: For the following function, describe the concavity and find relative extrem using the concavity test…

A:

Q: Suppose the slope of the curve y = f'(x) at (4, 7) is §. Find f'(7).

A: Given slope of the curve y=f-1(x) at (4,7) is 45

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: 1 For f(x) -x² + x + 2, find: a) the equation of the line that is tangent to the graph of f at the…

A:

Q: For the below function, find the stationary point(s) and prove if a maximum, minimum, or a saddle…

A: The given function is fx,y=-x2+6xy+y2-10x-5y. Compute the first and second partial derivatives as…

Q: Consider the function y = (-3x - 5)2. Using the values x = -8 and Ax = -0.5, calculate A y - dy.…

A: Given:  y=-3x-52x=-8△x=-0.5 We have to find △y-dy.

Q: Ex(20):- Locate all relative maxima and minima of f (x, y) = (x – 2)² + (y+1)² ¬

A: Find the all relative maxima and minima of f(x,y)=(x-2)2+(y+1)2 now find  fx=2(x-2) and fy=2(y+1)…

Q: determine the slope function S(x) for f(x)= lxl

A:

Q: Pls help on this question. ASAP

A: Given the function f(x) = -x2 + 5 We need to find slope of the secant of f(x) between x= -2 and x =…

Q: Find the function f given that the slope of the tangent line at any point (x, f(x)) is f'(x) and…

A:

Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: Given the derivative f'(x), find the x-value for all relative extrema for the graph of the original…

A: Consider the given derivative. f'x=x2−5x+6 Put the first derivative equal to zero.…

Q: Find thie avevage rate of change of flal with espect to x on the interval. F(x)=x² -5;[-4.0]

A:

Q: Use the limit formula for the derivative of a function at a point to find f'(-3) for f(r) = 2r2 – r.

A: use limit definition to find the value of derivative.

Q: Use the First Derivative Test to find the x-value(s) at which the function f(a) = + 4x? 2 9x? + 4…

A:

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: Examine the following functions for maxima-minima and trace the curves. a. Y = x* +1 a²x b. Y=-…

A:

Q: The derivative of f is xʻ(x-2Xx+3). At how many points will the graph of ƒ have a relative maximum?…

A:

Q: Let f be the linear function f(x) = -3x + 7. (a) The rate of change of f is (b) The graph of f is a…

A: Objective is to fine the rate of change , slope and y-intercept Intercept.

Q: -3. For the function f(x) = -5x - 3, find the slope of the tangent line at x =

A: We can find the slope in the following steps.

Q: A coffee company has found that the marginal cost, in dollars per pound, of the coffee it roasts is…

A:

Q: This is what I have so far but it says I am missing something.

A:

Q: Find the relative extrema of the function and classify each as a maximum or minimum. (Use either the…

A:

Q: Given the graph of the function f(x) below, estimate the derivative of the function at z = -2.…

A: As we know that, The derivative of the function at a point is equal to the slope of the tangent line…

Q: Let f(x) =4x divided by x -3. Find the slope of the secant lines on the graph of F through P(5, 10)…

A: f(x)=4x/(x-3) P(5,10) and Q (6, a)  (say) a= f(6)= 24/3 =8  Q(6,8) is

Q: f'(x) represents the slope of the secant line at any point on the graph of the function.

A:

Q: arke

A: please refer to the image below

Q: Find the slope of the secant line between x = 3 and x = 4 for the function f(x) = −x² − 2x + 4.…

A:

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: 8. Given the function f(x)%=2x3 -5x3 , find the point where the tangent is horizontal to the curve.

A:

Q: Complete the full analysis of the following exercises: 1- y = e* (x² - 3) The full analysis consist…

A:

Q: Find the following characteristics about the linear function 2 f(x) = ²/x + 18 x-intercept:…

A:

Q: Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Given,  f(x)=2 cos(3x)

Q: Suppose that f(x)=-7x2 + 8 (A) Find the slope of the line tangent to f(x) at x=2 (B) Find the…

A: To determine the following for the function f(x) = -7x2 + 8:Part a) Slope of tangent at x = 2.Part…

Q: Suppose f(x) = x^3 . Using the definition of derivative, compute both f'(x) and f''(x). (Hint: You…

A:

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: Let f (2) = 2 22 +6 x + 5 . We will use the definition of derivative to find the deivative of f (æ)

A:

Q: Find the linear approximation of the function below at x = -1 and use it to approximate f(-0.8). -7x…

A:

Q: Use the slopes of tangents to determine whether the function -6x2+36x is increasing, decreasing, is…

A: Given function, f(x)=-6x2+36x We know that function is said to be increasing when f'(x)>0, and…

Q: For the following exercises, use the second derivative test to identify any critical points and…

A: according to our guidelines we can answer only three subparts, or question and rest can be…