Math  /  Calculus

Question2. (a) A curve is defined by the function y=x33x5y=x^{3}-3 x-5
Find i) the gradient of the curve at the point where x=2x=2 ii) the coordinates of the maximum and minimum turning point (b) Obtain from first principles the derivative of the function y=2x2+4x3y=2 x^{2}+4 x-3 (c) Use integration by substitution to find the given integral 01(3x2+2)4dx\int_{0}^{1}\left(3 x^{2}+2\right)^{4} d x (d) Use the product rule to find dydx\frac{d y}{d x} given i. y=(3x2+1)(5t8)y=\left(3 x^{2}+1\right)(5 t-8) ii. y=t2sinty=t^{2} \sin t

Studdy Solution
Apply the product rule.
dydx=(2t)(sint)+(t2)(cost) \frac{dy}{dx} = (2t)(\sin t) + (t^2)(\cos t)
dydx=2tsint+t2cost \frac{dy}{dx} = 2t \sin t + t^2 \cos t

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