Consider the function f(x) 2x3 5x on the interval [-4,4]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one C in the open interval (-4, 4) such that f(c) is equal to this mean slope. For this problem, there are two values of C that work. The smaller one is and the larger one is

Q: Given the function f(x) = x³ - 3x2 x – 1, determine all coordinate points (x, y) on the graph of f…

A: The derivative of the function will give the value of slope. For two value of x, f(x) will have…

Q: The critical points of the function f(x) = a2– 14x + 12 are

A: Given function is f(x) = x2 - 14x + 12 Critical point of the function is the point in the domain…

Q: For the function y = (x − 2) In x, what are the two x intercepts, and between the two intercepts, is…

A:

Q: Find the local extreme values of the function: f(x,y)=xy-x^2-y^2-3x-3y+12.

A: It is given that, fx,y=xy-x2-y2-3x-3y+12We have to find the local extreme values.

Q: Find the critical points of the function f(x)=x4−5x4+5x3−1.

A:

Q: Find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)=−2x2+2x+3.

A: We have to find  the slope of the secant line between x=2 and x=5 on the graph of the function…

Q: Given the function g(x) = (x – 1)(z + 2)(z - 3) its g-intercept is its -intercepts are

A:

Q: The critical points of the function f(x)= 3x -36x+1 are

A: The critical points of a function are the points at which the function is defined but its derivative…

Q: Determine all the critical points for the function. f(x)=6x^5+33x^4−30x^3+100

A: We have to determine all the critical points for the function  f(x) = 6x5 + 33x4 - 30x3 + 100 We…

Q: For the function f(x)=x^3−27x, its local maximum is __ which occurs at (___; its local minimum is __…

A: To find the local maximum and local minimum for the function f(x) = x3 – 27x

Q: Given the function​ f, find the slope of the line tangent to the graph of f-1 at the specified point…

A: Obtain the inverse of the given function as follows:

Q: Find all points on the graph of ​f(x)=8x^2−26x+21.   where the slope of the tangent line is 0. The​…

A: Given : f(x) = 8x^2-26x+21 Find: All points where The slope tangent line is zero. We know tha slope…

Q: Find the slope of the secant line between x=−2 and x=3 on the graph of the function f(x)=−2x2 −5x+1.

A: The point on the graph when x =-2 is given by plugging x=-2 in the function:Hence, the point on the…

Q: Find the absolute maximum and absolute minimum values of the function: f(x)=5x^7−7x^5−7 on the…

A: We find the critical points by solving f'(x)=0 Use power rule to find f'(x)

Q: Find the critical points of the function f(K)-7x2-14x.

A:

Q: find the slope of the secant line between x=−1 and x=1 on the graph of the function…

A: Given that the secant line passes between the point x=-1 and x=1 on the function f(x)=-x3-3x2-2x+1.…

Q: Find the slope of the secant line between x = -1 and x = 2 on the graph of the function f(x) = -2x +…

A: The given function is fx=-2x3+3. Compute the slope of as follows.

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: )For the function f(x) = x-48x, its local maximum is which occurs at ( ... its local minimum is…

A: Solve by derivative test

Q: Given the function f, find the slope of the line tangent to the graph of f -1 at the specified point…

A: Given, The function is f(x)=(x+2)2 and the point on the graph of f-1(x) is (36,4).

Q: For the function f(x) = (3x^3) - (2x) on the interval [-2,2]. What is the average or mean slope of…

A: Obtain the slope of the function on the interval as follows.The given function is f(x) = 3x3 – 2x…

Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−2x3 +3.

A: Given lines are x = –1 and x = 2. Given function is

Q: Suppose f is a linear function such that f(3) = 9 and f(8) = 5.0. What is the slope m of f?

A: Given query is to find the slope of the function.

Q: The slope of the line tangent to the graph of f(x) = 19 – 4x² at the point x = -9 18 8 O 152 72 144

A: Given that: f(x)=19-4x2

Q: Find the slope of the function f (x) = x 3 + 3x 2 + 3x + 1 at x = 0 1 0 3

A:

Q: Find the point at which the line f(x) = - x – 2 intersects the line g(x) 3x + 6 %3D

A: f(x) = g(x) Thus, -x-2 = 3x + 6   Separate variables to LHS and constants to RHS -x-3x = 6 + 2 -4x =…

Q: Consider the function f(x)=3x^3−2x on the interval [-2,2]. Find the average or mean slope of the…

A: The objective is to find the mean value of the function and find the values of c for which f'(c) is…

Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−3x3+4x2+2.

A:

Q: Let f(x) = x2. Give an equation of the line that intersects the graph of f(x) at x = 0 and x = V2.

A: Given data:     The given function is: f(x)=x2. The first value of x is: x1=0. The second value of x…

Q: Consider the function f(x)=2x^3-9x^2-60x+2 on the interval [-6,8]. Find the average or mean slope of…

A: Given - f(x) = 2x3 - 9x2 - 60x + 2 ................... (1)  Interval =  [-6, 8] f(-6) =…

Q: Find the slope of the curve f(x)= x2 at the point P(2,4)

A:

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

A: we will find slope of secant line by two point slope formula

Q: given the function f(x)=axln(x+b), where function is decreasing at x=1-b?

A:

Q: Find the slope of the secant line between x = -1 and x = 2 on the graph of the function f(x) = 5x° –…

A: Given function is f(x)=5x3-5x2+2x+3

Q: Consider the function f(x) = 2x interval - 2, 2|. Find the average or mean slope of the function on…

A:

Q: Find the critical points of the function f(x) = 2x3 + 3x2 − 12x + 5.

A:

Q: Find the slope of the secant line between x=3 and x=5 on the graph of the function f(x)=−2x^2+2x+5.

A:

Q: The critical points of the function f(z) = 9x² - 8x + 16 are

A:

Q: Given the function f(x) = (x – 4)(x + 5)(x – 2) its f-intercept is Enter a point [more..]| its…

A: The objective is to find x intercept and x intercept

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: Revenue function, R(x)=-49x3+4x2+8, 0≤x≤5 To find the diminishing return, we shall use second…

Q: Find the values of x for all points on the graph of f(x)=x3-2x2+5x-16x at which the slope of the…

A: The given function is

Q: Find the point at which the line f(x)=−5x−3f(x)=-5x-3 intersects the line g(x)=−x+1g(x)=-x+1

A: The given functions are fx=-5x-3gx=-x+1

Q: Find all critical points for the function f(x) = x³ – 3x2 +5.

A: To find the critical point of the function             f(x) = x³ -3x² +5 For critical point we want…

Q: Evaluate the slope of the function: a. f(x) =x^2 + x - 2                              at x = -1.5…

A: Here we have to find the slope of the given different functions.

Q: find all the values of x at which the curve has a slope of -1. f(x) = 5 +x -3x^2

A: Given function, fx=5+x-3x2 And slope = - 1 i. e. f'x=-1

Q: Find the slope of the secant line between x=-4 and x=7 for f(x)=7x+9

A: The secant line between x=-4 and x=7 for f(x)=7x+9.

Q: Let: f(x)=2x3−3x2−12x+6.   a. Find all points on the graph of​ f(x) at which the tangent line is…

A: fx=2x3-3x2-12x+6 Slope of the tangent line is the derivative of the given function. So…

Q: Find the global extrema of the function f(x)=3x4−6x2+2 on the interval [−2,2]

A: Global extrema of a function exists at critical points or at the end points of the interval.…

Q: The function f (x) 4 +3 3x2 + 20 has all the following critical points except 3 -- (А) 4 (в) 2 -3

A: For critical points put first derivative=0

Q: The range of the function y= 16-x2 is the interval [0, 0)

A: