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A curve has parametric equations: x = 3t +8, y = t^3 - 5t^2 + 7t. Find the co-ordinates of the stationary points.

First differentiate: dx/dt = 3, dy/dt = 3t² - 10t + 7

Using the chain rule: dy/dx = dy/dt * dt/dx = (3t² - 10t + 7)/3

At stationary points, the...

Answered by Robbie B. • Maths tutor

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Integrate tan (x) with respect to x.

I = ∫ Tan (x) dx= ∫ (sin(x)) / (cos(x)) dx

We see that this is close to the standard integral ∫ F'(x) / F(x) dx = Ln (F(x)) + C

Answered by Matthew H. • Maths tutor

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Find the tangent to y = x^2 - 4x + 9 at the point (3,15)

First find dy/dx:

dy/dx = 4x - 4

And thus at (3,15):

dy/dx = 12 - 4 = 8 = m (as m is the gradient of a curve)

So using y - y₁ = m(x - x₁) where...

Answered by Scott H. • Maths tutor

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Find the derivative (dy/dx) of the curve equation x^2 -y^2 +y = 1.

Most of the differentiation problems require us to apply one of the well known rules, be it product rule, quotient rule or chain rule. But those problems have one thing in common: explicite formula for y...

Answered by Adam G. • Maths tutor

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The equation of a line is y=3x – x^3 a) Find the coordinates of the stationary points in this curve, stating whether they are maximum or minimum points b) Find the gradient of a tangent to that curve at the point (2,4)

a) A stationary point is any point on the curve that is flat, still, not increasing or decreasing. Another way to think of this is the gradient at a stationary point = 0

Firstly make an equation fo...

Answered by Lauren C. • Maths tutor

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