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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
Figure 6.84 A hyperbolic cosine function forms the shape of...
- 1.2 Basic Classes of Functions
This function cannot be written as a formula that involves...
- 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.
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.
Free Functions Average Rate of Change calculator - find function average rate of change step-by-step
22 kwi 2021 · Find the average rate of change of a function. Use a graph to determine where a function is increasing, decreasing, or constant. Use a graph to locate local maxima and local minima. Use a graph to locate the absolute maximum and absolute minimum. Gasoline costs have experienced some wild fluctuations over the last several decades.
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.
29 gru 2020 · We just found that \(f^\prime(1) = 3\). That is, we found the instantaneous rate of change of \(f(x) = 3x+5\) is \(3\). This is not surprising; lines are characterized by being the only functions with a constant rate of change. That rate of change is called the slope of the line.
