Question

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1. The gradients of the curve y = ax^2 + bx, where a
and b are constants, at the points x = 1 and x = 3
are -2 and 10 respectively. Find the value of a and
of b.​

Answer 1

Step-by-step explanation:

d/dx [ax² + bx] = 2ax + b.

When x = 1, 2a(1) + b = -2. => 2a + b = -2

When x = 3, 2a(3) + b = 10. => 6a + b = 10

Therefore a = 3 and b = -8.