Question

Find the slope of normal to the curve y= x^3+1 at origin.​

Answer 1

Answer:

y=f(x)=x3+2xy=f(x)=x3+2x

The first derivative of a function gives the slope of its curve at any given x-value.

This is the function’s first derivative, f′(x)f′(x):

f′(x)=3x2+2f′(x)=3x2+2

Evaluate the first derivative for the x-value of the point in question, (x=-1).

f′(−1)=3(−1)2+2f′(−1)=3(−1)2+2

f′(−1)=3(1)+2=5f′(−1)=3(1)+2=5 ← slope at x=-1

So, we know now that, at the point (−1,−3)(−1,−3), the slope of the curve is y=3x2+2y=3x2+2 = 5.