Find the equation of the the tangent to the curve y=x^3 - 7x + 3 at the point (1,2)
yC=x3 - 7x + 3 ------> equation of curve.yT=mx+c ----------------> equation of tangent, where m is the gradient of the graph and c is the value of the y-intercept (the value of y when x=o)To find m, you must take the differential of curve, and substitute the value of x from (1,2) into it.m=3x2 -7, m= 3(1)2 -7, m=-4Now, the equation of the tangent looks like yT=-4x+C.In order to find C, Subsitute the values of the (2,1) in for x and y.2=-4(1)+C2+4=C, C=6Therefore the function of the tangent is yT=-4x+6
MB
Related Maths A Level answers
All answers ▸Find the turning value of the following function, stating whether the value is min or max, y = x^2 -6x + 5
A curve C is mapped by the equation ( 1+x)(4-x). The curve intersects the x-axis at x = –1 and x = 4. A region R is bounded by C and the x-axis. Use calculus to find the exact area of R.
How do you find the coordinate of where two lines intersect?
June 2008 C1 Paper Differentiation Question