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In this section we look at some applications of the derivative by focusing on the interpretation of the derivative as the rate of change of a function. These applications include acceleration and velocity in physics, population growth rates in biology, and marginal functions in economics.
- 4.4 The Mean Value Theorem
Figure 4.25 The Mean Value Theorem says that for a function...
- 3.7 Derivatives of Inverse Functions
We begin by considering a function and its inverse. If f (x)...
- 4.5 Derivatives and The Shape of a Graph
Using the First Derivative Test. Consider a function f f...
- 4.7 Applied Optimization Problems
Identify the domain of consideration for the function in...
- 6.9 Calculus of The Hyperbolic Functions
If a cable of uniform density is suspended between two...
- 1.2 Basic Classes of Functions
1.2.1 Calculate the slope of a linear function and interpret...
- 4.4 The Mean Value Theorem
Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line. Predict the future population from the present value and the population growth rate. Use derivatives to calculate marginal cost and revenue in a business situation.
Free Functions Average Rate of Change calculator - find function average rate of change step-by-step
9 paź 2015 · You are correct. The gradient at a point will give you the direction of maximum increase in the value of the function. Its direction will be $\frac{\nabla f}{|\nabla f|}$ In your case: $$\nabla f = (12x^2yz^2+2z^3+yz,4x^3z^2+xz,8x^3yz+6xz^2+xy)$$ Therefore, $$\nabla f(1,-1,-1) = (-13,3,13)$$ As you have already calculated.
Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line. Predict the future population from the present value and the population growth rate. Use derivatives to calculate marginal cost and revenue in a business situation.
Find the average rate of change of a function. Since functions represent how an output quantity varies with an input quantity, it is natural to ask about the rate at which the values of the function are changing. For example, the function \ (C (t)\) below gives the average cost, in dollars, of a gallon of gasoline \ (t\) years after 2000. \ (t\) 2.
16 lis 2022 · The first tells us how to determine the maximum rate of change of a function at a point and the direction that we need to move in order to achieve that maximum rate of change. Theorem
