Question

Find an equation for the tangent line at the point where x=2 on the graph of the function f(x)=5^x/2

Answer 1

The slope of the tangent line is the derivative evaluated at the point.
Do you know how to find the derivative of your function? (And is that \(\frac{5^x}{2}\) or \(5^{\frac{x}{2}}\)?

Answer 2

no, I couldn't figure out how to find the derivative. Btw the function is 5^(x/2)

Answer 3

The derivative of \(a^x\) is \(a^x\ln{a}\).

Answer 4

So the derivative of your function is \(\frac{1}{2}5^{\frac{x}{2}}\ln{5}\)

Answer 5

where did the 1/2 come from?

Answer 6

The derivative of \(\frac{x}{2}\) is \(\frac{1}{2}\).

Answer 7

(You need to use the chain rule in the exponent.)

Answer 8

ok thank you!

Answer 9

how do you find the equation?

Answer 10

Find f(2), you'll get the coordinates of a point.
Find f'(2), you'll get the slope of the tangent line.
Equation of the tangent line can thus be obtained by the point-slope form.