Using Derivatives to Find Tangent Line and Rate of Change
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(3) Find the equation of the line tangent to g(x) = -6x + 64sqrt(x) at x = 16.
(4) Find the average rate of change of h(x) = -3x^4 + 14x^2 + 22x from x = -3 to x = 5.
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Solution Summary
In this solution we show how to use derivatives to solve for the tangent line and rate of change.
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Find the slope of the tangent line by finding the derivative of g(x) and plugging in x = 16:
Original: g(x) = -6x + 64x^(1/4)
Derivative: g'(x) = -6 + (1/4)(64)x^(1/4 - 1)
g'(x) = -6 + 16x^(-3/4)
Plug in 16: g'(16) = -6 + 16(16)^(-3/4)
g'(16) = -6 + 16(1/8)
g'(16) ...
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