Find the gradient of the curve y = sin(2x) + 3 at the point where x = pi
This is a question that relates to the topic of differentiation. Typically students encounter this topic near the end of the first term of the first year of their A Level.The equation of the curve, y = sin(2x) +3 needs to be differentiated to find the general gradient of the line.
This uses the chain rule which is [f(g(x))]' = f'(g(x))g'(x)
The equation is, therefore, differentiated in two parts.[sin(2x)]' = cos(2x) x 2 = 2cos(2x)[+ 3]' = 0
Therefore the general gradient of the curve is: d/dx = 2cos(2x)
The question asks for a specific gradient, at point when x=pi. Therefore, we substitute the value of x=pi into the equation.
d/dx = 2cos(2pi) = 2 x 1 = 2
Therefore, the gradient of the curve at the point where x=pi is 2
AS
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