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Find the equation of the tangent line to the curve when x has a given value.?
f(x)=x^3/4 ; x=4
a.y=32x+12
b.y=4x-32
c.y=4x+32
d.y=12x-32
1 Answer
- Anonymous10 years agoFavorite Answer
First you differentiate f(x), then evaluate the derivative at x=4. This will give you the slope (m) of the tangent line. You are now finished with the derivative; just keep that value of m handy.
Go back to the original function and evaluate it at x=4 to get the y-coordinate. So now you have the coordinates of a point on the line, (4, f(4)), and the slope of the line, m. You use those in the definition of slope to find the y-intercept, b.
m = (y2 - y1) / (x2,x1)
m = (f(4), - b) / (4 - 0). Rearrange this to solve for b
b = f(4) - 4m
Finally, plug your values for m and b into the good old y = mx + b equation. It should resemble one of the above choices.