The profit in dollars from the sale of x expensive watches is P(x)= 0.09x-3x+4x°4 -4400. Find the marginal profit when (a) x = 300, (b) x= 2000, (c) x = 5000, and (d) x= 12,000. %3D (a) When x= 300, the marginal profit is $. (Round to the nearest integer as needed.)

Q: Find the point (x,y) at which the graph of y=4x2 +4x-8 has a horizontal tangent line

A:

Q: 5. Find an equation of the line tangent to the curve y = 3x² 1 and parallel to the line 2x – y + 3 =…

A: Explained below

Q: Find h'(-2) if h = f • g, f(x) = -6x2 – 4 and the equation of the tangent line of g at -2 is y = -9x…

A: Slope of y=-9x+6 is = -9 This line is tangent to g at x=-2  So we get: g'(-2)= -9   The tangent line…

Q: For which value(s) of x does f(x)=−x^3/3−2x^2+3x−8 have a tangent line of slope 7?

A:

Q: 4. At what point on the graph of y =x2 is the tangent line parallel to the line 2x – 4y = 3?

A:

Q: Find an equation of the line tangent to f(x) = xcos x at x=-4. (Round coefficients to 3 decimal…

A:

Q: 3. Find the slope m of the tangent lines to the parabola y = -x+ 5x+ 6t its point of intersection…

A:

Q: Find all points (x, y) on the graph of ƒ(x) = 3x2 - 4x with tangent lines parallel to the line y =…

A: Since the tangent is parallel to y = 8x + 5. Hence, the slope of the tangent = slope of the line = 8

Q: The curve y = ax² + bx + c passes through the point (2, 28) and is tangent to the line y = 4x at the…

A:

Q: Find all the points on the curve x² y² + 2xy = 3 where the slope of the tangent is -1. O (1,1) O…

A: We have find possible point where the slope of the tangent is -1

Q: Find the point where the line tangent to y=x* – 3x² +2 at (2, 6) crosses the x – axis.

A: y=x4-3x2+2,  2, 6 Differentiating with respect to x, we get dydx=4x3-32x+0=4x3-6x Now slope of the…

Q: The equation of tangent line to the graph of 8x²+16y²=48 at (2,1) is A x- y - 3=0 x- y+3=0 c none of…

A: Slope of tangent line is y'

Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

Q: 10. Find the slope-intercept form of the equation of the line tangent to the graph of y arctan(9x)…

A: Given y = arc tan9xand x=39here we find the slope - intercept form of the equation of the line…

Q: Find the slope of the curve y = 2x(x-1)° at point (1,-1). %3D O -1 O 4 O 2 O -2 O 1

A:

Q: f the line tangent to the graph of y =x* – 2x + 1 at x =-1

A: Idea: find the slope of tangent line by differentiation at x=-1 .then find the point on the curve.…

Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: Explanation: Given that,  y=2x3-3x2-10x+1     Concept Used: 1. Slope of the tangent is the first…

Q: Find the slope of the line tan gent to the curve of 2y³ + xy + 1 = 0 at the point (-3, 1) .

A:

Q: 2.) What is the equation of the line tangent to y(x) x- 2r3+6x-3 at r =-1?

A: Follow the steps .

Q: Find the equation of the tangent line to the curve x2 + 4y2 = 8 and parallel to the line x+2y=8.

A: Given curve is x2+4y2=8. To find equation of tangent line to the given curve which is parallel to…

Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: What is the slope of the tangent line that touches the graph of In y + e2z-1 = 3y – 4x at the point…

A: Given that: lny+e2x-1=y-4x

Q: Where does  f(x) = x^3-3x^2+2x-7 have tangent lines that are parallel to y=2x-7?

A: We have to find the coordinates of point at which f(x)=x3-3x2+2x-7 have tangent lines that are…

Q: Find the point (x,y), at which the graph of y = 8x+6x-3 has a horizontal tanger The function y= 8x…

A: Our Aim is to find the point (x,y) at which the graph of y=8x2+6x-3-(i)has a horizontal tangent.

Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

Q: Find the slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

A:

Q: 2. Find the length of the curve y=- 1 from 1<x<2. 8 4x?

A:

Q: find the slope of the curve x = e^-tcost2t, y=e^-2tsin2t at the point t= 0

A: find out the slope of the curve at t=0

Q: 25. Find the equation of the line tangent to the curve x2 + y2 = 1 through the point (,).

A:

Q: (3) Find an equation of the tangent line to the curve y = 2x² + 3 that is parallel to the line %3D…

A:

Q: 3. Find the equation of the tangent to y = 1-x² 3x+7 at the point where x = 1.

A:

Q: find equation of both the tangent lines to the elipse x^2+4y^2=36 that pass through the point(12,3)

A:

Q: At what values of x on the curve y= 2x³+13x²+5x+9 does its tangent lines pass through the origin? In…

A: Given equation of curve: y=2x3+13x2+5x+9……1

Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

A:

Q: Find an equation of the tangent line to the graph at the given point.

A: Given, fx=4xx2+6 Now we find the slope ddx4xx2+6 Now by using the quotient rule,…

Q: The slope of the tangent to the curve yx + y²x² -6 at (2,1) is

A:

Q: Find the slope of the line tangent to the curve x^3 - 3xy + 4x = 2 at x=1.

A:

Q: a) Find the slope of the tangent to the curve y = 3+ 4x2 – 2x³ at the point where x = a.

A: We are suppose to solve the problem by application of derivative.   NOTE :: As per our guidelines we…

Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2

A: Consider the function  y=3x(cosx) Point : π2,π2

Q: Find a point on the graph where x = t² - 1, y = 2t has a vertical tangent.

A: For vertical tangents dx/dy=0

Q: Find all points (x, y) on the graph of f(x) = x° - 5x + 26x + 19 with tangent lines parallel to the…

A:

Q: 5. Find the point on the parabola y=-x+3x+4 where the slope of the tangent line is 5.

A:

Q: The slope of the line tangent to the curve y = x*- 8x3 + 22x² – 24x + 9 at x = 1 is _.

A:

Q: Find equation of a line tangent to the graph: f(x) = xm) at xo = 1

A:

Q: Find the equation of a tangent line to the curve y= 2x3 - 3x² - 10x + 1 which is perpendicular to…

A:

Q: Find the slope of the line tangent to the curve y = cos2 x at the point(−π/3 , 1/4)

A:

Q: The slope of the tangent to the curve y²x + y²a² = 6 at (2, 1) is A B) -1 в 14

A: We can find the slope of the tangent to the curve at the indicated point as below.

Q: Find

A:

Q: 4. Find the slope of the line tangent to the graph of the equation -ey +y° = 7+ 2x at the point…

A: Given query is to find the slope of the tangent at given point.

Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: