FInd the Line Tangent to the graph y=f(x) through the point P given: f(x)=10^x and P(0,1)

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FInd the Line Tangent to the graph y=f(x) through the point P given: f(x)=10^x and P(0,1)

[From: ] [author: ] [Date: 11-09-11] [Hit: ]

y = ln(10)*x + 1-Find the slope of the tangent line by choosing a point close to the one you are given. Use the slope to write the equation of the tangent line by the point slope formula (y-y1)=M(x-x1).......

i know that the point is P(a,f(a)) and that the derivative of 10^x is 10^x(ln10)..

im not sure if the derivative helps but i could use some help.. Thanks

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f(x) = 10^(x)

f '(x) = 10^(x) * ln(10)

f '(0) = slope of tangent = ln(10)

Eqn of tangent line:

y - 1 = ln(10)*x

y = ln(10)*x + 1

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Find the slope of the tangent line by choosing a point close to the one you are given. Use the slope to write the equation of the tangent line by the point slope formula (y-y1)=M(x-x1).

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since you know f'(x) = 10^x(ln10)
slope is f'(0) = 10^0 (ln10) = ln10
y -1 = ln10 (x - 0)
y = ln10 x +1

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