What's the gradient of the curve y = 2t^4 + 3t^3 - t + 4 at the points

1.	What's the gradient of the curve y = 2t^4 + 3t^3 - t + 4 at the points (0, 4) and (1, 8)?
Answer» First, differentiate the function: 8t³+9t²-1 which gives us the gradient at any point. When t=0, the function is 4 and when t=1, the function is 2+3-1+4=8 which confirms that the given points are on the curve. We only need the t value to find the gradient at the given points, so at t=0 the gradient is -1 and at t=1 it's 8+9-1=16.

What's the gradient of the curve y = 2t^4 + 3t^3 - t + 4 at the points (0, 4) and (1, 8)?

Answer»

First, differentiate the function: 8t³+9t²-1 which gives us the gradient at any point.

When t=0, the function is 4 and when t=1, the function is 2+3-1+4=8 which confirms that the given points are on the curve.

We only need the t value to find the gradient at the given points, so at t=0 the gradient is -1 and at t=1 it's 8+9-1=16.

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What's the gradient of the curve y = 2t^4 + 3t^3 - t + 4 at the points (0, 4) and (1, 8)?

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