4. Refer to functions f(x) = Vx+ 20 and g(x)= x² - 9 a. Find the function (x) and write its domain in interval notation. Use functions f(x) = Vx+20 and g(x)=x² -9 to answer questions b, c, and d. b. Find (fog)(5). Give exact simplified answer. Find (g·f)(-4). Give exact simplified answer. c. d. Find (f +g)(16). Give exact simplified answer.

Q: Calculate the approximation for the given functionand interval:                    M4, f (x) =√x,…

A:

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

A:

Q: ) Find a function ƒ such that f'(x)= x³ +3 and such that the line y+5x O is tangent to the graph of…

A: Given, f'(x) = x3+3  and the line  y +5x =0 is tangent to the graph of f   Let's assume the function…

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: a) Find the points on the graph of f(x) = 2x- 3r²- 12x + 8 where the tangent is 3. horizontal.

A:

Q: For what values of x does the graph of f(x)=2x^3+15x^2−36x−5 have a horizontal tangent line?

A:

Q: Suppose that f is a function given as f(x)=x3+bx2+cx−4 Find the exact values of b and c if we know…

A: Given: fx=x3+bx2+cx-4   and tangent line y=36x+68

Q: If f is a function defined by the equation y = f1x2, then x iscalled the variable, and y is…

A: Given: If f is a function defined by the equation y = f(x), then x is called the _________ variable,…

Q: a. Find the inverse of the function ƒ(x) = mx, where m is a constant di«erent from zero.b. What can…

A: To find :   a) The inverse of the function f(x) = mx, where m is a constant different from…

Q: There is no point on the graph of f(x) = 3x2 4 at which the tangent line is y = 12x- 2. Select one:…

A: We have to consider gi condition is true or false

Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: Find a function f such that f (x) = 2x3 and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A: Key point used: The slope m, of the tangent to f(x) at point h,k, is equal to f'x=h. Given:Eq of…

Q: For what values of æ does the function f (x) = 12x – æ³ have a horizontal tangent line? Select all…

A: The given function is fx=12x-x3

Q: Find the absolute extrema of the function on the closed interval.

A: Solution Given Find the derivative of the functionf'(x)=xx2+1To find the criticle Number derivative…

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

A:

Q: Which type of discontinuity does the function S4- a², In x, x < 1 f(x) = 1<x < e has at x 1?

A: We need to choose correct option.

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is:

A: Given f(x) = ex - 1

Q: Find a function f such that f'(x) = 2x³ and the line 54x + y = 0 is tangent to the graph of f. f(x)…

A:

Q: The best suitable method to approximate a zero of the function f(x) = e* – 1 is: |

A: Given,                 f(x)=ex-1

Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   =&gt; the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

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: Please

A: For concave downward, f''(x) &lt; 0 f(x) = (1-1/x)2 = 1 - 2/x + 1/x2 f'(x) =2/x2 - 2/x3 f''(x) =…

Q: State the interval of the function g(x) = E-x is %3D

A: The given function is gx=32-x  exist in the interval (-∞,32] and does not exist in any other…

Q: Find the values of a and b so that f will be differentiable at x = 3.

A:

Q: 1 Find the distance between the two values of x at which the function is discontinuous. x²-3x + 2

A: The function given is ,f(x) = 1x2-3x+2f(x) is discontinous when,x2-3x+2 = 0Using quadratic formula,x…

Q: Find dydx, where y is defined as a function of x implicitly by the equation below. y3+2x2y5=1

A:

Q: Calculate the approximation for the given function and interval.                         M6, f (x) =…

A:

Q: What happens to the function f (x) = 1 + as x approaches to zero.

A: The definition of the function gx=x is given by, gx=x for x≥0=-x for x&lt;0 Thus, the left hand…

Q: The slope of the line tangent to the graph of f(x) = 18 – 5x² at the point x = -8 O 20 O 10 O 160 O…

A:

Q: Determine if the given function is differentiable at a = 1 4 – 2x, if x 1

A:

Q: given that the graph of f(x) passes through the point (10,9) and the slope of its tangent line…

A:

Q: Find the extreme values of the function x²y with respect to x + y = 5

A:

Q: Also, suppose that T (x, y) = x³y² + 35 is the function that models the plate temperature in D.…

A:

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = V f(x), evaluate…

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: Find and classify the extreme point of the function f(x, y) 3y2x + x³ - 3y3 - 3x? + 2.

A:

Q: - Find the domain of the following functions: a- y=2x. y = (x+1) c-y = - Vx+4 (3-х)

A:

Q: Find an equation of the line tangent to the graph of f(x) at the point (5,9): f(x) = e-3x-1o + 8

A:

Q: The graph of f (x) = ax+b x²+3x-8 has horizontal tangent at (2, -1). Determine the values of a and…

A: Given query is to find the value of a and b.

Q: Find the equation of the tangent line to the graph of the function f(2)=√1026 +26 at the point…

A:

Q: Write the equation of the line tangent to the graph of f (x) = -3x² + 5x + 1 at x = 1 and use it to…

A: We have to find the tangent line equation and also we have to approximate f(1.2).

Q: The equation of the tangent line for the function f(x) = -8 – 5x at a = 8 is %3D y = -5(x + 8) + 48…

A: Given that      f(x) = -8 -5x at x = 8 We have to find the equation of the tangent line for the…

Q: For the function f(z) = ¹, the point z 1-e Z = 0 is

A:

Q: 2. Sketch the graph of the function (b) ƒ(x, y) = Vx² + y? – 1 -

A: our objective is to draw the graph.

Q: What is the x-value associated with the extreme point of the following function: 1*1.1^x+ 1*0.2^x?

A: Given Data: Function: fx=1×1.1x+1×0.2x The derivative of the given function is,…

Q: Find a function f such that f '(x) = 5x3 and the line 40x + y = 0 is tangent to the graph of f. f(x)…

A:

Q: Find y' if 3x2- (ry?) = 2y.

A: Given that, 3x2-xy212=2y3 Find the derivative of the given equation.

Q: Consider the function f(x, y) = 4x² – 8y² subject to the condition x + y = 25.

A:

Q: Find the line tangent to the function at the indicated point: f(x) = v8x² – 4x ;x = 1 ОУ-12х-10 o…

A: Since there are multiple questions present and you have not specified which question to answer,…