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 ▸Solve the following pair of simultaneous equations: 2x - y = 7 and 4x + y = 23
Let R denote the region bounded by the curve y=x^3 and the lines x=0 and x=4. Find the volume generated when R is rotated 360 degrees about the x axis.
What is the derivative with respect to x of the function f(x)=1+x^3+ln(x), x>0 ?
What is 'e' and where does it come from?