What is the slope of the parabola #y= -1/3x^2 +23x/3 -85/3# at the point (7,9)? Calculus Derivatives Tangent Line to a Curve 1 Answer Bill K. Jun 1, 2015 The derivative is #y'=-2/3 x+23/3#. Therefore the slope of the graph of the function at #x=7# is #y'(7)=-2/3\cdot 7+23/3=-14/3+23/3=9/3=3#. 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 1988 views around the world You can reuse this answer Creative Commons License