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Complete Question
Find the general expression for the slope of a line tangent to the curve of y=2x^2+4x at the point P(x,y) . Then find the slopes for and x=0.5. Sketch the curve and the tangent lines. What is the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) ?
Answer:
The generally expression for the slope of is
The graph is shown on the first uploaded image
The generally expression for the slope of is
Step-by-step explanation:
From the question we are told that
The equation of the curve is
First we differentiate the equation
So
Therefore the generally expression for the slope tangent to the curve is
The next step is to substitute for x = 3 and x = 0.5
So for
And for
Here m_1 and m_2 are slops of the curve
Next we obtain the coordinates of the tangent lines
So at
So the coordinate for the first tangent line is
At
=>
So the coordinate for the second tangent line is
Next we obtain the equation for the tangent lines
So generally the slope is mathematically represented as
For and
=>
For and
Generally the general expression for the slope of a line tangent to the curve of the function y=2x^2+4 at the point P(x,y) is mathematically evaluated by differentiating y=2x^2+4 as follows
