Find the gradient of the line Y = X^3 + X + 6 when X = 4
Step 1: Differentiate the equation Y = X^3 + X + 6 to find the gradient of the line at any point. To do this, multiply each term of X by the old power and -1 from that power. This makes dy/dx = 3X^2 + 1.Step 2: As X=4, Substitute all terms of X with 4. This means that the gradient at the point (4,3) = 3(4)^2 + 1 = 49.
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