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excellence1 · Feb 25, 2016

how to differentiate loge(x-x^2)

B) Find the equation of the curve tha f''x = 12ex^2 and a stationary point at (0,3)

integral95 · Feb 25, 2016

Using the log rule for differentiation d/dx ln(f(x)) = f'(x)/f(x)

$\frac{d}{dx} ln(x-x^2) = \frac{\frac{d}{dx}(x-x^2)}{x-x^2} = \frac{1-2x}{x-x^2}$

integral95 · Feb 25, 2016

excellence1 said:
how to differentiate loge(x-x^2)

B) Find the equation of the curve tha f''x = 12ex^2 and a stationary point at (0,3)

$f''(x) = 12ex^2 \\ \\ \therefore f'(x) = \int 12ex^2 = 4ex^3+C$

Now since the point (0,3) is a stationary point that means

$f'(0) = 0 = 4e(0) + C \Rightarrow C = 0 \\ \\ \therefore f'(x) = 4ex^3$

$f(x) = \int 4ex^3 = ex^4 + C$

since the point (0,3) exist on f(x), then

$f(0) = 3 = e(0) + C \\ \\ C = 3 \\ \\ \\ f(x) = ex^4+3$

and that's the equation of the curve

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