Simple Calculus question. (1 Viewer)

[enigma_1]

Hey, please help

QUESTION: Find the gradient of the secant between (1,2) and the point where x = 0.999 on the curve y=x^4 +1

Then, use this to find the gradient of the tangent to the curve y=x^4 +1 at the point (1,2).

Thanks.

 

[hit patel]

For the secant sub in 0.999 in dy/dx=4x^3 to get the gradient 3.988

Then sub in 0.999 in y=x^4+1 to get the y value on the curve where x=0.999 . The y value at this point is y= 1.996

Now use one point formula to find the equation of two coordinates (0.999,1.996) and gradient 3.988.

y-1.996=3.988(x-0.999)
y=3.988x-1.988





To find gradient of tangent to curve at point (1,2)
dy/dx=4x^3

Sub 1 into dy/dx to find gradient=4
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