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Question Number 129052 by oustmuchiya@gmail.com last updated on 12/Jan/21
$${Let}\:\boldsymbol{\mathrm{p}}\:{and}\:\boldsymbol{\mathrm{Q}}\:{be}\:{points}\:{on}\:{the}\:{curve} \\ $$$$\boldsymbol{{y}}=\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}\:{while}\:\boldsymbol{{x}}=\mathrm{2}\:{and}\:\boldsymbol{{x}}=\mathrm{2}+\boldsymbol{{h}} \\ $$$$\boldsymbol{{respectively}}.\:\boldsymbol{{E}}{press}\:{the}\:{gradient} \\ $$$${of}\:\boldsymbol{\mathrm{P}}{Q}\:{in}\:{terms}\:{of}\:\boldsymbol{{h}}. \\ $$
Commented by benjo_mathlover last updated on 12/Jan/21
$$\mathrm{P}\left(\mathrm{2},\mathrm{0}\right);\:\mathrm{Q}\left(\mathrm{2}+\mathrm{h},\mathrm{h}^{\mathrm{2}} +\mathrm{2h}\right) \\ $$$$\mathrm{gradient}\:\mathrm{of}\:\mathrm{PQ}\:=\:\frac{\mathrm{h}^{\mathrm{2}} +\mathrm{2h}−\mathrm{0}}{\mathrm{2}+\mathrm{h}−\mathrm{2}}=\frac{\mathrm{h}^{\mathrm{2}} +\mathrm{2h}}{\mathrm{h}}=\mathrm{h}+\mathrm{2} \\ $$