The gradient of the tangent to the curve of y = 60x + 3x² - 4x³ at the point where x = 1 is 54
Step-by-step explanation:
To find the gradient of a tangent of a curve at point (a , b)
∵ The equation of the curve is y = 60x + 3x² - 4x³
- Find y'
∵ The differentiation of 60x is 60
∵ The differentiation of 3x² is 6x
∵ The differentiation of -4x³ is -12x²
∵ y' = 60 + 6x - 12x²
- To find the gradient of the curve at x = 1 substitute x by 1 in y'
∵ m = 60 + 6(1) - 12(1)²
∴ m = 60 + 6 - 12
∴ m = 54
The gradient of the tangent to the curve of y = 60x + 3x² - 4x³ at the point where x = 1 is 54
Learn more:
Learn more about differentiation in brainly.com/question/4279146
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