Given that y = 60x + 3x^2 - 4x^3, calculate:(a) the gradient of the tangent to the curve of y at thepoint where x = 1
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A:
The gradient of the tangent to the curve of y = 60x + 3x² - 4x³ at the point where x = 1 is 54Step-by-step explanation:To find the gradient of a tangent of a curve at point (a , b)Differentiate the equation of the curve to find y'Substitute the value of x in y' by a to find the gradient of the tangent (m)Remember that the differentiation of [tex]ax^{n}[/tex] is [tex]anx^{n-1}[/tex]∵ 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 = 54The gradient of the tangent to the curve of y = 60x + 3x² - 4x³ at the point where x = 1 is 54Learn more:Learn more about differentiation in brainly.com/question/4279146#LearnwithBrainly