Final answer:
To find the slope of the tangent to the curve y = 34x² - 2x³, you need to find the derivative of the equation. The derivative of y = 34x² - 2x³ is 68x - 6x². Plug in the value of x at the point you want to find the slope to get the slope of the tangent line.
Step-by-step explanation:
To find the slope of the tangent to the curve y = 34x² - 2x³, we need to find the derivative of the equation. The derivative of the equation y = 34x² - 2x³ can be found by applying the power rule and the constant rule. The power rule states that the derivative of x^n is nx^(n-1), and the constant rule states that the derivative of a constant times x is just the constant. So, taking the derivative of y = 34x² - 2x³, we get dy/dx = 68x - 6x².
Now that we have the derivative, we can plug in the value of x at the point we want to find the slope. Since we want to find the slope at a specific point, let's say x = a, we substitute a into the derivative equation dy/dx = 68x - 6x². So, the slope of the tangent line at x = a is 68a - 6a².