Introduction to Derivatives
This worksheet introduces grade 10 students to the fundamental concepts of derivatives in calculus, including limits, slopes of tangent lines, and basic differentiation rules.
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Introduction to Derivatives
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What does the derivative of a function represent graphically?
The area under the curve
The y-intercept of the function
The slope of the tangent line to the curve
The maximum value of the function
2. The limit definition of the derivative is given by:
lim (h→0) [f(x+h) - f(x)] / h
lim (h→0) [f(x) - f(x+h)] / h
lim (h→∞) [f(x+h) - f(x)] / h
lim (h→0) [f(x) + f(h)] / h
1. The process of finding the derivative of a function is called .
2. If a function is differentiable at a point, it must also be at that point.
1. Using the power rule, find the derivative of the function f(x) = x^3 + 2x - 5.
2. Explain in your own words what a limit is in calculus.
1. The derivative of a constant function is always zero.
True
False
2. A function can have a derivative at a point where it is not continuous.
True
False
Consider the graph of the function f(x) below:
1. Sketch the graph of the derivative, f'(x), on the same coordinate plane or a new one provided.