Homework Soursefind and equation of the tangent line to the curve fxintegra
find and equation of the tangent line to the curve f(x)=integral(e^t^2dt) at the point x=1
Solution
According to the Fundamental Theorem of Calculus, f\'(x) = e^(x^2).
Find the slope of the tangent line:
m = f\'(1) = e^(1^2) = e^1 = e
Find the equation of the tangent line:
y - y0 = m(x - x0)
y - f(1) = e(x - 1)
y = e(x - 1) + f(1)
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