Chain Rule & Integration by Substitution
Package of problems

Odd one out
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Warm-up

Look at the following three functions. What’s the same and what’s different about them?

\[y=(x+1)^2 \quad \quad y= \tan x \quad \quad y= x^3+1\]

Find a reason why each one is the odd one out of the three.

  • Which functions have graphs which pass through \((0,0)\)?

  • Which functions have graphs with stationary points?

  • Which functions are always increasing?

  • Which functions are odd?

  • Which functions can be thought of as compositions of functions?

  • Which functions have \(\dfrac{dy}{dx}=0\) when \(x=0\)?

  • Which functions have \(\dfrac{d^{2}y}{dx^{2}}=0\) for some value of \(x\)?

Can you find any more reasons?

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Last updated 04-Nov-16
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