Question: A curve C has equation y = x 3 5x 2 + 5x + 2. a. Find dy/dx in terms of x. b. The

A curve C has equation y = x³ − 5x² + 5x + 2.

a. Find dy/dx in terms of x.

b. The points P and Q lie on C. The gradient of C at both P and Q is 2. The x-coordinate of P is 3.

i. Find the x-coordinate of Q.

ii. Find an equation for the tangent to C at P, giving your answer in the form y = mx + c, where m and c are constants.

iii. If this tangent intersects the coordinate axes at the points R and S, find the length of RS, giving your answer as a surd.

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a To find dydx we need to differentiate the equation y x3 5x2 5x 2 with respect to x Taking the derivative term by term we have dydx ddxx3 ddx5x2 ddx5... View full answer

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