Find the tangent to the curve y=x^3+3 at the point x=1.
1. Differentiate the Equation of the curve to find the gradient: y'=3x^2
2. The gradient of the tangent is found by substituting x=1 into y'=3x^2: Gradient of tangent=3
3. Now we must find out the co-ordinates of the point. These are (x=1, y=1^3+3) = (1,4).
4. Now to find out the equation of the tangent, substitute x=1, y=4 and m=3 into y=mx+c to get c=1, (the y-intercept)
5. This gives the tangential equation as y=3x+1.
SK
Related Maths A Level answers
All answers ▸Integrate ln(x) by parts then differentiate to prove the result is correct
The function f (x) is defined by f (x) = (1-x)/(1+x), x not equal to -1. Show that f(f (x)) = x. Hence write down f ^-1 (x).
What is the derivative of x^x
Find the derivative of f(x)=exp((tanx)^(1/2))