At the point (0, 3) on the curve y=x33+x2−3x+3; the gradient of the curve increasing

y=x33+x2−3x+3⇒dydx=x2+2x−3=mdmdt=(2x+2)dxdt at(0,3)dmdt=2dxdt

At the point (0, 3) on the curve y=x33+x2−3x+3; the gradient of the curve increasing

y=x33+x2−3x+3⇒dydx=x2+2x−3=mdmdt=(2x+2)dxdt at(0,3)dmdt=2dxdt

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At the point (0, 3) on the curve $y = \frac{x^{3}}{3} + x^{2} - 3 x + 3;$ the gradient of the curve increasing

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3 times as fast as x

2 times as fast as x

equally as fast as x

None

answer is B.

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$y = \frac{x^{3}}{3} + x^{2} - 3 x + 3 \Rightarrow \frac{d y}{d x} = x^{2} + 2 x - 3 = m$

$\frac{d m}{d t} = (2 x + 2) \frac{d x}{d t} a t (0, 3)$

$\frac{d m}{d t} = 2 \frac{d x}{d t}$

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At the point (0, 3) on the curve y=x33+x2−3x+3; the gradient of the curve increasing

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At the point (0, 3) on the curve $y = \frac{x^{3}}{3} + x^{2} - 3 x + 3;$ the gradient of the curve increasing