Use the function f(x)=x^2-4 and g(x)=2x+20 and answer (a) (a) Solve g(x)<=0. What is the correct answer in interval notation?

Q: How is the graph off (x) = x 3 - l2x 2 + 36x - 16 related to the derivative f'(x) = 3x 2 - 24x + 36?

A:

Q: Differentiate the function using the three step rule. Show your solution. f(x)=(x)/(√(x-4))

A: You must have idea about three step differentiation method.

Q: Find the second derivative of the function. f(x) = (3x5 + 6)6

A: topic - double derivative

Q: What are the x- and y-intercepts of a function, and how are they found?

A: The x-intercept is the length from origin to where the graph of the function cut the x-axis.   The…

Q: Find the points of inflection given the function: Given the function f(x) = 2x³+ 3x²-12x-9 Where…

A: For the inflection point, second derivative is equal to zero.

Q: Express as an interval: {x : |x − 5| &lt; 4}

A: Given expression:  {x : |x − 5| &lt; 4} |x − 5| &lt; 4 x = ?  as an interval.

Q: find the derivative  f(x)= (2x-3)6(3x+4)

A: Given function is f(x)=(2x–3)^6(3x+4). Formulas used:

Q: Express the fact that x differs from - 1 by less than 1 as aninequality involving an absolute value.…

A: Express the fact that x differs from - 1 by less than 1 as aninequality involving an absolute value.…

Q: What is the equation of the line passing through the vertices of the graphs of the functions f(x) =…

A:

Q: -1 c) lim x+4+ √16x²

A:

Q: How do you find the 17th derivative of f(x)=2x^15-13x?

A: We can find the 17th derivative as below.

Q: determine the positive and negative intervals of the equation f(x)=x2e17x

A: Note that x2≥0 for all x. And, e17x&gt;0 for all x.   That means f(x)=x2e17x≥0 for all x.

Q: Find the second derivative. f(x) = 5x10 - 19x5 – 11x3 + 2 f"(x) =

A:

Q: Find an equation for the line tangent to f(x)=x3 +3x2 -2x-8, at the point where x=1

A: To find the equation of the tangent line at point x = 1 for the given curve.

Q: solve for first and second derivative (x2 + 8)2(x − 8)

A: Let

Q: The absolute value function increases on the interval ____________and decreases on ____________ .

A: The absolute value function increases on the interval  0, ∞ and decreases on -∞, 0 .

Q: Use the definition of the derivative to solve.

A: Given,

Q: X -2

A:

Q: Find the second derivative  X3 + 4x2

A:

Q: 20053x-1-0

A: in problem (b)   2cos2x - 1 =0cosx = 12

Q: Apply the second derivative test to find the relative extrema of the function fx) =x*-18x-3

A:

Q: find the derivative f(x)=(2x3-3)2/3

A: Consider the given function

Q: Find the derivative:   f(x) = (4x3-7x+9)5

A: Given:  fx=4x3-7x+95 To Find: The derivative of the given function

Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: Find the higher-order derivative. F'(x) - 7x* - 8x? + 5x f"(x) =

A:

Q: The graph of f(x)=2x^3+6x^2−144x+6 has two horizontal tangents. what are the positive and negative…

A: See the details solution in below

Q: Solve using the crossing-graphs method. Express to two decimal places. 20/9+4x=x

A:

Q: Find the second derivative. 14) y = 4x² + 12x + 4x-3

A:

Q: f(x) = (4x³ + 6x +1)°

A: To find the derivative of,  f(x) = (4x3 + 6x + 1)9

Q: Find the equation of the secant line on the graph of the function f(x)=7x2 between the points where…

A: take x=-1 . take x=5

Q: Find the second derivative  3x2/3/ 6x+ 9

A: Let the given function be y - y = 3x236x+9y = 12x23-1+9y = 12x-13+9Differentiating with respect to…

Q: Find the second derivative x4/7 -( solve using rationalising)

A: From the given problem:   fx=x47   As we know the second derivative is represented by:…

Q: Sketch the curve. Show your solutions. f(x) = x4 - 6x2

A: Consider the given: fx=x4−6x2Apply exponent rule:     ab+c=abacfx=x2x2−6x2Factor out common term…

Q: Use the second derivative test to find the local extreme values of y= 2x7-x+12

A:

Q: A paper airplane was thrown from the top of a 9 meter tall house and falls at a rate of 3 meters…

A: Given  The height of the paper airplane above the ground can be found using  the function  y  =…

Q: find horizontal and vertical intercept of f(x)= -2|x+1|+6 and graphing the function

A: The given function:

Q: use the second derivative test to find and characterize all the relative extremes of f(x)=2x4-24x3+4

A:

Q: For function, find the point in the graph at which the tangent line has slope 9 Y= -0.025x^2+6x What…

A: The given function is:Y=-0.025x2+6xThe slope is 9

Q: The derivative of f(x) = 10 (x2 + 13z) is О 10х + 130 О 10х ?(2т + 13) O 10 O -10x 3(2x + 13) O -…

A:

Q: Find the domain of the function. (Enter your answer using interval notation.) g(x) = /x+ 5 --

A:

Q: How do I express x=-10,2   in interval notation?

A:

Q: 1 f(x)3= 8x

A:

Q: Use the second derivative test to find the extreme values of the function f(x) = x³ – 3x? – 24x . -

A:

Q: Calculate the derivative. f (x) = 2x3 − 3x2 + 5

A:

Q: 9. Suggest a function that would have a derivative of f'(x) = 24x² + 6x – 10. Explain how you…

A: The derivative of a function id given as f'(x)=24x2+6x-10......(1)

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.