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Calculus

1. Find an equation for the line tangent to y= -5-5x^2 at (5,-130)

2. Find the slope of the function's graph at the given point. Then find an equation for the line tangent to graph:
f(x) = x^2 + 2, (-2,6)
What is the slope of the function's graph at the given point?

3. Using the defenition, calculate the derivative of the function:
g(t)= 9/t^2
Calculate: g'(-2), g'(1), g(sqrt 6)

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4. Find y by applying the Product rule, and then find y by multiplying the factors to produce a sum of simpler terms to differentiate:
y=(3x^2 + 4) (2x-7+6/x)

5. Suppose that the dollar cost of producing x appliances is c(x)=1100 + 60x-0.2x^2.

(a) Find the average cost per appliance of producing the first 130 appliances.
(b) Find the marginal cost when 130 appliances are produced
(c) Show that the marginal cost when 130 appliances are produced is approximately the cost of producing one more appliance after the first 130 have been made, by calculating the latter cost directly.

Solution Preview

Dear student, please refer to the attachment for the solutions. Thank You.

Equation of Tangent at (a, b) to a given curve f(x), is given as: (y-b) = f' (a)(x-a)
y = -5 -5x2

y^'=dy/dx=(-5)(2x)=-10x

Therefore, the equation of the tangent at the point (-5, 130) to the line y = -5 -5x2
is given as:
(y-130) = y'(-5) {x-(-5)}
Or, ...

Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problems and provides students with a clear perspective of the underlying concepts.

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