A profit is earned when revenue exceeds cost. Let the profit function for a skateboard manufacturer be given by P(x) = 30x - 0.3x2 - 250, wherlx is the number of skateboards sold. (a) P'(x), the marginal profit. (b) Use the marginal profit to estimate the profit from the sale of the 11th skateboard.

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A: We have  y=ax2+bx+c        at (2,28)           and               y=4x

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A: Given ellipse equation is x236+y216=1 find the slope of the tangent line at the point (x,y)

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Q: 6. A rancher wants to fence off a rectangular corral with an area of 4050 sq. yds next to a river.…

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A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

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Q: Determine the slope of the line tangent to y = x+1 at x = 1 3x2

A: y = (x+1)/3x2 slope = dy/dx dy/dx = (3x2(1) - 6x(x+1))/9x4 slope at x=1 dy/dx = (3 - 6(2))/9 dy/dx =…

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Q: F(x) = -7+ x2 INTERUAL-ピ-3 -2. AUERAGE RATE of

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Q: What is the slope of the line tangent to the graph of g(x)=1/x at x=1?

A: Given that ,         g(x)=1x          find slope of tangent at x=1

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A: Given function is  fx at x=a

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Q: 1. What is the instantaneous slope of y = 5 at x = 5?

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Q: Determine the gradient of the straight line which is tangent to the graph of f(x)= tan^-1(ln x) at…

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Q: Find the slope of the line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

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

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Q: 2. Use an example to show how to use the First Derivative Test for critical points

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Q: Find the point(s) on the curve where the tangent line is horizontal i.e. slope is zero). 3 (x+x²' f…

A: Solution below  Slope is zero at a point where dy/dx=0

Q: Determine the x-values where relative extrema occur for y = (x² +x – 12). Use the second- derivative…

A: Here y=x2+x-122 ⇒y'=ddxx2+x-122       =2x2+x-12ddxx2+x-12       =2x2+x-12(2x+1) for critical points,…

Q: X where tangent line is horizontal. f(x)=x3-4x2-9x+13

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Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

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Q: How do you find the partial derivative of a given function using the definition formula?

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Q: Explain how to determine Partial derivatives for x-value ?

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Q: Find the points on the graph of f where the tangent line is horizontal.  f(x)=(x^2+8)(5-x) larger…

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Q: Use the second derivative test to find all relative extrema  f(x)= x+4/x

A: The given function is as - f(x) = x+4xProcedure to find local extremas - 1. Find f'(x)2. Put f'(x) =…

Q: The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor…

A: A. Profit Function : P(X) = R(x) - C(x) P(x) = -0.04x2 + 800x - 130x + 40000 P(x) = -0.04x2 + 670x +…

Q: How does the partial derivative relate to the limit of a function of two variables?

A: Solution

Q: The derivative of the function y=f(x) at the point x=c is characterized as the of the function at…

A: We have to tell what is derivative of function y=f(x) at x=c called ...  a. Slope  b. Point of…

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Q: Explain whether the Quotient Rule should be used to find the partial derivative

A: Partial Differentiation:     ∂∂x(xyx2+1)ddx(uv)=v.dudx-u.dvdxv2

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Q: Estimate the slope of the tangent to the function f(x) = (x + 1)^2(x - 4) at the point of abscissa…

A: Introduction: A tangent line is one that intersects a curve at the so-called point of tangency.…