Calculus Question

Question

Use first principle to determine the equation of tangent to f(x)=3x²- 6.

Answer 1

first derivative = 6x = slope of the quadratic = slope of the tangent line

tangent line is a linear equation: y=6x + b. to solve for b, you need to know the point where the tangent line touches the parabola, or know some point on the tangent line

If you just knew the x value of the tangency point, such as for example x=1

then (1,-3) is where the tangent line touches the parabola and

then -3 =6+b, b =-9 and the tangent line is y=6x-9