A curve has equation y = 7 - 2x^5. a) Find dy/dx. b) Find an equation for the tangent to the curve at the point where x=1.
a) The derivative dy/dx of the equation is: dy/dx = -10x4. If you don't remember this, revise Power Rule for derivatives.b) The equation of a line is given by y = mx + q. To find the tangent line at a point, we need: 1) Find the slope of the line by substituting that point in the equation of the derivative m = dy/dx (x=1) = -10. 2) Solve the system between the curve and the line at x=1 to find q. We find q=15. The equation of the line is therefore: y = -10x + 15
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