How do you find the equation of a line tangent to the function y=x^3+6 at (1,7)? Calculus Derivatives Tangent Line to a Curve 1 Answer Alberto P. Nov 7, 2016 y=3x+4 Explanation: The tangent equation is y-f(x_0)=f^'(x_0)(x-x_0) Then f(x_0)=7, f^'(x)=3x^2, f'(x_0)=f^'(1)=3 so the tangent is y-7=3(x-1) y=3x+4 Answer link Related questions How do you find the equation of a tangent line to a curve? How do you find the slope of the tangent line to a curve at a point? How do you find the tangent line to the curve y=x^3-9x at the point where x=1? How do you know if a line is tangent to a curve? How do you show a line is a tangent to a curve? How do you find the Tangent line to a curve by implicit differentiation? What is the slope of a line tangent to the curve 3y^2-2x^2=1? How does tangent slope relate to the slope of a line? What is the slope of a horizontal tangent line? How do you find the slope of a tangent line using secant lines? See all questions in Tangent Line to a Curve Impact of this question 1540 views around the world You can reuse this answer Creative Commons License