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- dy b) Find the equation of a curve if gradient of the curve at point (x, y) is given by- = 2x3 + x and dx point (2, 3) lies on the curve.3. Consider the function f(z, y) = r'y - 4y at the point P(2, -1). (a) Find the dlirectional derivative of the function at the point P in the direction of the vector = (2,5). (b) In what direction does f have the maximum rate of change? What is the maxi- mum rate of change?Find the point where the tangent line to the curve c(t) = (8t2 – 6, 3t2 – 12t) is horizontal. (х, у) %3D Find the point where the tangent line is vertical. (x, y) = ( _
- Please show your answers to at least 4 decimal places. Find the directional derivative of the function f(x, y) = ln (x³ + y5) at the point (-3,2) in the direction of the vector (2, 1).Find the unit tangent vector to the curve defined by 7(t) = (3 cos (t), 3 sin(t), 5 sin (t)) at t = 3 *() 3 Use the unit tangent vector to write the parametric tions of a tangent line to the curve at t = 3 *(t) = y(t) = z(t) = TEFind an equation of the tangent line to the curve 2(r² + y')² = 25(z² – y) (a lemniscate) at the point (-3, 1). An equation of the tangent line to the lemniscate at the given point is