Find the derivative of this function at a specific point [closed]

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What is the derivative of $$f(t)= \frac{t^3 +2} t$$ at point $(-2,3)$.

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2 Answers

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Lets take the derivative of the function according to the definition so we have:

$$f'(-2)=\lim_{x\to -2}\frac{f(x)-f(-2)}{x-(-2)}$$ if the limit exists. So we should do: $$f'(-2)=\lim_{x\to -2}\frac{\frac{x^3 +2} x-3}{x+2}=\lim_{x\to -2}\frac{x^2-2x+1}{x}=-9/2$$

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$$f(t)=t^2+\dfrac{2}{t}$$ so $$f'(t)=2t-\dfrac{2}{t^2}$$ so $$f'(-2)=2\cdot (-2)-\dfrac{2}{(-2)^2}=-4-\dfrac{1}{2}=-\dfrac{9}{2}$$

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