# calculus

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determine the slope of the tangent for the following function. Then determine the equation of the tangent line at x=1

F(x) = x
F(x) = x^4

• calculus -

For F(x) = x, the first derivative - which is the slope of the line tangent to a curve - would be:
F'(x) = 1

For the second part, it doesn't matter what value x is, F'(x) is always 1.

For F(x) = x^4, the first derivative - which is the slope of the line tangent to a curve - would be:
F'(x) = 3x^3

For the second part, you just plug in 1 for x:
F'(x) = 3(1)^3 = 3

• calculus -

The second function's derivative is wrong. Brain fart on my part.

For F(x) = x^4, the first derivative - which is the slope of the line tangent to a curve - would be:
F'(x) = 4x^3

For the second part of the question, you just plug in 1 for x:
F'(x) = 4(1)^3 = 4

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