Use local linear approximation to estimate the value of the given quantity: (1.01)^15.

Okay, so I know that the formula I need is
f(x + h) ≈ f(x) + h(f'(x))
and that I need to set up the problem first, like this:
f(x)= x^15 x= 1

f'(x)=15x^14 h= .01
I'm a bit confused as to how I should go about solving this. If someone could walk me through this problem and tell me if I'm on the right track or not I would greatly appreciate it.

Question

Use local linear approximation to estimate the value of the given quantity: (1.01)^15.

Okay, so I know that the formula I need is 
f(x + h)  ≈ f(x) + h(f'(x))
and that I need to set up the problem first, like this:
f(x)= x^15                    x= 1

f'(x)=15x^14                 h= .01
I'm a bit confused as to how I should go about solving this. If someone could walk me through this problem and tell me if I'm on the right track or not I would greatly appreciate it.

phi · Answer

Find the slope at x=1

anonymous · Answer

Really? I thought I would plug in the values and go from there?

anonymous · Answer

Kind of like this?

(1.01)^15 ≈ x^15 + .01 (15x^14)

phi · Answer

almost.
you want to evaluate at x=1

We start with the curve
y= x^15
and we figure out the equation of the tangent line  (at some point we are interested in)
the line is easier to evaluate than the curve, so we use the line *instead of the curve*
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