Mark44 said:Use the fact that (2, 4) is a point on the curve in your given equation, which will give you an equation that involves only a and b.
Then use the fact that at x = 2, dy/dx = 8 in your equation for the derivative. This will give you another equation in a and b.
Finally, solve the two equations in a and b simultaneously.
danago said:Have another look at the first equation.
No.tweety1234 said:is it meant to be [tex] 32a + b =4 [/tex] ?
Differentiation is a mathematical process that involves finding the rate of change of a function with respect to its independent variable. It is used to calculate the slope of a curve at any given point and is an important concept in calculus.
Differentiation is important because it allows us to understand and analyze the behavior of a function. It helps us to find maximum and minimum values, calculate rates of change, and solve optimization problems in various fields such as physics, economics, and engineering.
Differentiation and integration are inverse operations of each other. While differentiation calculates the slope of a curve, integration calculates the area under the curve. In simpler terms, differentiation is finding the rate of change while integration is finding the accumulation.
The most commonly used methods of differentiation are the power rule, product rule, quotient rule, and chain rule. These rules provide a step-by-step process for finding the derivative of a function.
Differentiation has various real-life applications, such as determining the velocity and acceleration of an object in physics, finding the marginal cost and revenue in economics, and analyzing the growth and decay of populations in biology. It is also used in engineering to optimize designs and in finance to calculate rates of return and risk management.