Let . Answer the…

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Let f(x)=3x3−5x+2x2+1f(x)=\dfrac{3x^{3}-5x+2}{x^{2}+1}. Answer the following. (i) Show that f(x)f(x) is differentiable for all real xx. (ii) Find f′(x)f'(x). (iii) Calculate f′(1)f'(1). (iv) Hence write the equation of the tangent to the curve y=f(x)y=f(x) at the point where x=1x=1.

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