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Show that the curve $ y = 2e^x + 3x + 5x^3 $ has no tangent line with slope 2.
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Calculus 1 / AB
Derivatives of Polynomials and Exponential Functions
Harvey Mudd College
University of Michigan - Ann Arbor
University of Nottingham
Idaho State University
In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.
In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.
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Hey, it's Claire. So when you're in here so our first gonna find the derivative in terms of X, we get to eat the X Plus three plus 15 X Square. Now he's stuck this equal to two. Since we're solving for a slope of two. When we see that there's no, um, solution, since the smallest the function can ever be is why is equal to three?
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