4) Consider the following function: y= x^4/3-x^3/3 +20 a) Find derivative and critical values. Draw a number line and show the intervals of where the Curve is rising and falling.    b) Find the 2nd derivative and possible inflection points. Draw a number line and show the Intervals of where the curve is concave up and concave down.   c) Sketch the curve below. Label relative max and min points and points of inflection.

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Q: 6. Find the tangent line and normal line to curve y = x3 - 3x2 - 2 at point (1, -4)?

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Q: #8.) Determine the slope of the tangent at point (1,4) on the graph of f(x) = (9-x²) ²/

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.