A curve is defined by the parametric equations x = 2t and y = 4t^2 + t. Find the gradient of the curve when t = 4
the gradient of the curve = dy/dx
and dy/dx = (dy/dt)(dt/dx)
dy/dt = 8t + 1
dx/dt = 2 therefore dt/dx = 1/2
dy/dx as above = (8t + 1) * 1/2 = (8t + 1)/2
where t = 4, dy/dx = (8*4 + 1)/2 = (32 + 1)/2 = 33/2
AB
Related Maths A Level answers
All answers ▸A projectile is thrown from the ground at 30 degrees from the horizontal direction with an initial speed of 20m/s. What is the horizontal distance travelled before it hits the ground? Take the acceleration due to gravity as 9.8m/s^2
What are volumes of revolution and how are they calculated?
Find the point of intersection of the lines y=2x-7 and 4y-2=3x
Solve the following simultaneous equations: y-3x+2=0, y^2-x-6x^2=0