3. Use calculus and algebraic methods to do a complete analysis (i.e., intervals of increase and decrease, intercepts, critical points, points of inflection, and intervals of concavity) for g(x) = (x +4)°(x +2). You DO NOT need to graph.

Q: 1. Sketch the curve by following the guidelines: a) domain, b) intercepts, c) symmetry, d)…

A: Domain set of all input values where function defined Range set of all output values

Q: C. If h(x) = [f(x)]² + g(x),what is the equation of the line tangent to the graph of h at x = -2?…

A: First we will find derivative of h(x) at x=(-2) that gives the slope of the required tangent.

Q: 2 Find an equation of the line L, where L is perpendicular to y =x and passes through the point…

A: Given a Line L which is perpendicular to  y = (2/3)x  at point (3,2)  Equation of line L is…

Q: Determine the missing coordinates of the points on the graph of the function.

A: The missing coordinates are given in the following graph as follows.

Q: Given that f(7) = 1 and f'(7) = -7, find an equation for the tangent line to the graph of y = f(x)…

A:

Q: (a) If g(x) = x2/3, show that g'(0) does not exist.(b) If a ≠ o, find g'(a).(c) Show that y = x2/3,…

A:

Q: For what values of a and b is the line – 3x + y = b tangent to the curve y = ax³ when x = 5? a = =

A: Given: Equation of curve is, y=ax3 The line tangent to the curve is, -3x+y=b at x=5. The objective…

Q: , Find the equation ofthe line thet Is tangent to graph of the giren functlon at the Point CC, fC)…

A: First you will find the slope of the tangent by using the fact that the derivative of the function…

Q: Given that f(2) =-7 and f'(2) = -8, find an equation for the tangent line to the graph of y = f(x)…

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: 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: y = f(x)

A: We can answer all the three questions as below.

Q: Please help me with x and y intercepts the critical values, and the inflection point for the…

A: To sketch the graph of the function.

Q: 98. Find the points on the graph of y = 2x6 – x* - 2 at which the tangent line is horizontal.

A: Find the points on the graph of  y=2x6-x4-2at which the tangent line is horizontal.

Q: For what values of a and b is the line – 2x + y = b tangent to the curve y = ax? when x = 3? - - a =…

A: Given: To determine the values of a and b is the line -2x+y = b tangent to the curve y=ax2 when x =…

Q: 4. Sketch the graph and find the relative extrema on the indicated interval: y = 4x1/3 + x1/3 [-2,2]

A:

Q: 3. Find the points of inflection: y = x- 2cosx

A: We have to find inflection point

Q: Given that f(4) = -8 and f'(4) = –6 , find an equation for the tangent line to the graph of y = f(x)…

A:

Q: 8. The line y = -4x + b is tangent to the curve f(x) = 2x² – 8x + 12. Determine the value of b. %3D

A: The equation of the tangent at a point h,k on a curve y=f(x) is given by, y-k=f'(h) (x-h)

Q: Among the solutions of the 3rd order linear ODE y"-y"+y'-y = 8et, only one function satisfies lim y…

A:

Q: 6. Find the length of the curve y =-+ from x =1 to x=2. 9. 28x

A: The curve is given by the equation, y=x99+128x7  and the point is given from x=1 to x=2. To find :…

Q: 2. Given the function, find the slope of the line tangent to the curve: f(x) = v5x + 2 at the point…

A: We have to find the slope of the line tangent to the curve: f(x)=5x+2 at the point P(1,2) for the…

Q: (1) If f(x)=(x-1)(x-3)(x-5),a%3D0,b=4. Find the value of csuch that f (c) has the same value as the…

A:

Q: 3. Find the points of inflection: y = x-2cosx

A: Explanation of the answer is as follows

Q: 3) Find all points (x, y) on the graph of x2/3+y²/3 = 8 where the tangent lines have slope –1.

A:

Q: find the length of the curve on the given interval: y = 4/3 (x+1) ^ (3/2), [0,3]

A:

Q: Grien that the graph of fx) passes throush the point (7,4) and that the slope of its tanger line at…

A: Given problem:- Given that the graph of f(x) passes through the point (7,4) and that the slope of…

Q: csec²x +secx -2=0 3cotx-3=0

A: Given: 3 cotx -3=0

Q: Given that f(2) = -5 and f'(2) = 3, find an equation for the tangent line to the graph of y = f(x)…

A: we have to find equation of tangent line

Q: If given f(3) = -1 and f'(3)=5, the tangent line to the graph y = f(x) at x=3 is y = 5x +16. (a)…

A: This question is based on finding tangent equation at a point on function.

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

Q: a) Given that straight line y + x=2 is tangent to the curve y =x² – 6x + q. Find value q.

A: Given,  y+x=2⇒y=-x+2

Q: The temperature of points on a plate x + xy+ y² < 1 is modeled by f(x, y) = 25(x² + y²). Find the…

A:

Q: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

A:

Q: 9. Find the points on the graph y = 7x - where the slope of the tangent line is parallel to x-2 28x…

A: To find- Find the points on the graph y = 7xx - 2 where the slope of the tangent line is parallel to…

Q: 2 For the graph of f(x) = ax + bx +4, the slope of the tangent at the point (3, 1) is 5. Determine…

A: Given that        f(x) = ax2+bx+4

Q: For what values of x does the graph of f(x) =x³ + 9x² +x + 5 have a horizontal tangent?

A: GIVEN : f(x) = x3 + 9x2 + x + 5

Q: Given that y" = 2x, find the value of y when x = 3 if the curve passes through the point (-1,); and…

A:

Q: I. Analyze and sketch the following curves. Indicate the intercepts, asymptotes, & critical points…

A:

Q: 19. For what values of the constants a and b is (1, 3) a point of inflection of the curve y = ax³ +…

A: Consider the value of y and solve:

Q: Consider the following. 2 X- 3 x² - 3 x (a) Find the points of intersection of the curves. (x, y) -…

A:

Q: csec?x +secX -2=0

A: Given equation sec2x+secx−2=0

Q: If f'(4)= 6 and g'(4)=3, then the slope of the tangent line to the graph of y=2f(x)-5g(x) at x=4 is…

A:

Q: 9) Find the point(s), if any, where the graph has a horizontal tangent for 3x4 %3D = - 3x2 f(x) = 4…

A:

Q: 2) Use DESMOS to graph Y = 10* + 3, show critical points. %3D

A:

Q: Substitute c = 2 in the formula for slope as follows. %3D + Ax) - g ( lim Ax- 0 m = Ax

A: We have to substitute in the slope formula.

Q: 10. Find the points of inflection of the curve y f(x)=x³ -x.

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…